path: root/feed 2.rss

<?xml version="1.0" encoding="UTF-8"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:content="http://purl.org/rss/1.0/modules/content"><channel><title>Navan Chauhan</title><description>Welcome to my personal fragment of the internet.</description><link>https://navanchauhan.github.io/</link><language>en</language><lastBuildDate>Sat, 18 Jan 2020 19:19:50 +0530</lastBuildDate><pubDate>Sat, 18 Jan 2020 19:19:50 +0530</pubDate><ttl>250</ttl><atom:link href="https://navanchauhan.github.io/feed.rss" rel="self" type="application/rss+xml"/><item><guid isPermaLink="true">https://navanchauhan.github.io/posts/2020-01-14-Converting-between-PIL-NumPy</guid><title>Converting between image and NumPy array</title><description>Short code snippet for converting between PIL image and NumPy arrays.</description><link>https://navanchauhan.github.io/posts/2020-01-14-Converting-between-PIL-NumPy</link><pubDate>Tue, 14 Jan 2020 00:10:00 +0530</pubDate><content:encoded><![CDATA[<h1>Converting between image and NumPy array</h1><pre><code><div class="highlight"><span></span><span class="kn">import</span> <span class="nn">numpy</span>
<span class="kn">import</span> <span class="nn">PIL</span>

<span class="c1"># Convert PIL Image to NumPy array</span>
<span class="n">img</span> <span class="o">=</span> <span class="n">PIL</span><span class="o">.</span><span class="n">Image</span><span class="o">.</span><span class="n">open</span><span class="p">(</span><span class="s2">&quot;foo.jpg&quot;</span><span class="p">)</span>
<span class="n">arr</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">img</span><span class="p">)</span>

<span class="c1"># Convert array to Image</span>
<span class="n">img</span> <span class="o">=</span> <span class="n">PIL</span><span class="o">.</span><span class="n">Image</span><span class="o">.</span><span class="n">fromarray</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
</div>

</code></pre><h2>Saving an Image</h2><pre><code><div class="highlight"><span></span><span class="k">try</span><span class="p">:</span>
    <span class="n">img</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">destination</span><span class="p">,</span> <span class="s2">&quot;JPEG&quot;</span><span class="p">,</span> <span class="n">quality</span><span class="o">=</span><span class="mi">80</span><span class="p">,</span> <span class="n">optimize</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">progressive</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
<span class="k">except</span> <span class="ne">IOError</span><span class="p">:</span>
    <span class="n">PIL</span><span class="o">.</span><span class="n">ImageFile</span><span class="o">.</span><span class="n">MAXBLOCK</span> <span class="o">=</span> <span class="n">img</span><span class="o">.</span><span class="n">size</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">img</span><span class="o">.</span><span class="n">size</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
    <span class="n">img</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">destination</span><span class="p">,</span> <span class="s2">&quot;JPEG&quot;</span><span class="p">,</span> <span class="n">quality</span><span class="o">=</span><span class="mi">80</span><span class="p">,</span> <span class="n">optimize</span><span class="o">=</span><span class="bp">True</span><span class="p">,</span> <span class="n">progressive</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
</div>

</code></pre>]]></content:encoded></item><item><guid isPermaLink="true">https://navanchauhan.github.io/posts/2019-12-22-Fake-News-Detector</guid><title>Building a Fake News Detector with Turicreate</title><description>In this tutorial we will build a fake news detecting app from scratch, using Turicreate for the machine learning model and SwiftUI for building the app</description><link>https://navanchauhan.github.io/posts/2019-12-22-Fake-News-Detector</link><pubDate>Sun, 22 Dec 2019 11:10:00 +0530</pubDate><content:encoded><![CDATA[<h1>Building a Fake News Detector with Turicreate</h1><p><strong>In this tutorial we will build a fake news detecting app from scratch, using Turicreate for the machine learning model and SwiftUI for building the app</strong></p><p>Note: These commands are written as if you are running a jupyter notebook.</p><h2>Building the Machine Learning Model</h2><h3>Data Gathering</h3><p>To build a classifier, you need a lot of data. George McIntire (GH: @joolsa) has created a wonderful dataset containing the headline, body and wheter it is fake or real. Whenever you are looking for a dataset, always try searching on Kaggle and GitHub before you start building your own</p><h3>Dependencies</h3><p>I used a Google Colab instance for training my model. If you also plan on using Google Colab then I reccomend choosing a GPU Instance (It is Free) This allows you to train the model on the GPU. Turicreat is built on top of Apache's MXNet Framework, for us to use GPU we need to install a CUDA compatible MXNet package.</p><pre><code><div class="highlight"><span></span><span class="nt">!pip</span><span class="na"> install turicreate</span>
<span class="na">!pip uninstall -y mxnet</span>
<span class="na">!pip install mxnet-cu100==1.4.0.post0</span>
</div>

</code></pre><p>If you do not wish to train on GPU or are running it on your computer, you can ignore the last two lines</p><h3>Downloading the Dataset</h3><pre><code><div class="highlight"><span></span><span class="nt">!wget</span><span class="na"> -q &quot;https</span><span class="p">:</span><span class="nc">//github.com/joolsa/fake_real_news_dataset/raw/master/fake_or_real_news.csv.zip&quot;</span>
<span class="nt">!unzip</span><span class="na"> fake_or_real_news.csv.zip</span>
</div>

</code></pre><h3>Model Creation</h3><pre><code><div class="highlight"><span></span><span class="kn">import</span> <span class="nn">turicreate</span> <span class="kn">as</span> <span class="nn">tc</span>
<span class="n">tc</span><span class="o">.</span><span class="n">config</span><span class="o">.</span><span class="n">set_num_gpus</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="c1"># If you do not wish to use GPUs, set it to 0</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">dataSFrame</span> <span class="o">=</span> <span class="n">tc</span><span class="o">.</span><span class="n">SFrame</span><span class="p">(</span><span class="s1">&#39;fake_or_real_news.csv&#39;</span><span class="p">)</span>
</div>

</code></pre><p>The dataset contains a column named "X1", which is of no use to us. Therefore, we simply drop it</p><pre><code><div class="highlight"><span></span><span class="n">dataSFrame</span><span class="o">.</span><span class="n">remove_column</span><span class="p">(</span><span class="s1">&#39;X1&#39;</span><span class="p">)</span>
</div>

</code></pre><h4>Splitting Dataset</h4><pre><code><div class="highlight"><span></span><span class="n">train</span><span class="p">,</span> <span class="n">test</span> <span class="o">=</span> <span class="n">dataSFrame</span><span class="o">.</span><span class="n">random_split</span><span class="p">(</span><span class="o">.</span><span class="mi">9</span><span class="p">)</span>
</div>

</code></pre><h4>Training</h4><pre><code><div class="highlight"><span></span><span class="n">model</span> <span class="o">=</span> <span class="n">tc</span><span class="o">.</span><span class="n">text_classifier</span><span class="o">.</span><span class="n">create</span><span class="p">(</span>
    <span class="n">dataset</span><span class="o">=</span><span class="n">train</span><span class="p">,</span>
    <span class="n">target</span><span class="o">=</span><span class="s1">&#39;label&#39;</span><span class="p">,</span>
    <span class="n">features</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;title&#39;</span><span class="p">,</span><span class="s1">&#39;text&#39;</span><span class="p">]</span>
<span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="o">+-----------+----------+-----------+--------------+-------------------+---------------------+</span>
<span class="o">|</span> <span class="n">Iteration</span> <span class="o">|</span> <span class="n">Passes</span>   <span class="o">|</span> <span class="n">Step</span> <span class="n">size</span> <span class="o">|</span> <span class="n">Elapsed</span> <span class="n">Time</span> <span class="o">|</span> <span class="n">Training</span> <span class="n">Accuracy</span> <span class="o">|</span> <span class="n">Validation</span> <span class="n">Accuracy</span> <span class="o">|</span>
<span class="o">+-----------+----------+-----------+--------------+-------------------+---------------------+</span>
<span class="o">|</span> <span class="mi">0</span>         <span class="o">|</span> <span class="mi">2</span>        <span class="o">|</span> <span class="mf">1.000000</span>  <span class="o">|</span> <span class="mf">1.156349</span>     <span class="o">|</span> <span class="mf">0.889680</span>          <span class="o">|</span> <span class="mf">0.790036</span>            <span class="o">|</span>
<span class="o">|</span> <span class="mi">1</span>         <span class="o">|</span> <span class="mi">4</span>        <span class="o">|</span> <span class="mf">1.000000</span>  <span class="o">|</span> <span class="mf">1.359196</span>     <span class="o">|</span> <span class="mf">0.985952</span>          <span class="o">|</span> <span class="mf">0.918149</span>            <span class="o">|</span>
<span class="o">|</span> <span class="mi">2</span>         <span class="o">|</span> <span class="mi">6</span>        <span class="o">|</span> <span class="mf">0.820091</span>  <span class="o">|</span> <span class="mf">1.557205</span>     <span class="o">|</span> <span class="mf">0.990260</span>          <span class="o">|</span> <span class="mf">0.914591</span>            <span class="o">|</span>
<span class="o">|</span> <span class="mi">3</span>         <span class="o">|</span> <span class="mi">7</span>        <span class="o">|</span> <span class="mf">1.000000</span>  <span class="o">|</span> <span class="mf">1.684872</span>     <span class="o">|</span> <span class="mf">0.998689</span>          <span class="o">|</span> <span class="mf">0.925267</span>            <span class="o">|</span>
<span class="o">|</span> <span class="mi">4</span>         <span class="o">|</span> <span class="mi">8</span>        <span class="o">|</span> <span class="mf">1.000000</span>  <span class="o">|</span> <span class="mf">1.814194</span>     <span class="o">|</span> <span class="mf">0.999063</span>          <span class="o">|</span> <span class="mf">0.925267</span>            <span class="o">|</span>
<span class="o">|</span> <span class="mi">9</span>         <span class="o">|</span> <span class="mi">14</span>       <span class="o">|</span> <span class="mf">1.000000</span>  <span class="o">|</span> <span class="mf">2.507072</span>     <span class="o">|</span> <span class="mf">1.000000</span>          <span class="o">|</span> <span class="mf">0.911032</span>            <span class="o">|</span>
<span class="o">+-----------+----------+-----------+--------------+-------------------+---------------------+</span>
</div>

</code></pre><h3>Testing the Model</h3><pre><code><div class="highlight"><span></span><span class="n">est_predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">test</span><span class="p">)</span>
<span class="n">accuracy</span> <span class="o">=</span> <span class="n">tc</span><span class="o">.</span><span class="n">evaluation</span><span class="o">.</span><span class="n">accuracy</span><span class="p">(</span><span class="n">test</span><span class="p">[</span><span class="s1">&#39;label&#39;</span><span class="p">],</span> <span class="n">test_predictions</span><span class="p">)</span>
<span class="k">print</span><span class="p">(</span><span class="n">f</span><span class="s1">&#39;Topic classifier model has a testing accuracy of {accuracy*100}% &#39;</span><span class="p">,</span> <span class="n">flush</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">Topic</span> <span class="n">classifier</span> <span class="n">model</span> <span class="n">has</span> <span class="n">a</span> <span class="n">testing</span> <span class="n">accuracy</span> <span class="n">of</span> <span class="mf">92.3076923076923</span><span class="o">%</span>
</div>

</code></pre><p>We have just created our own Fake News Detection Model which has an accuracy of 92%!</p><pre><code><div class="highlight"><span></span><span class="n">example_text</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;title&quot;</span><span class="p">:</span> <span class="p">[</span><span class="s2">&quot;Middling ‘Rise Of Skywalker’ Review Leaves Fan On Fence About Whether To Threaten To Kill Critic&quot;</span><span class="p">],</span> <span class="s2">&quot;text&quot;</span><span class="p">:</span> <span class="p">[</span><span class="s2">&quot;Expressing ambivalence toward the relatively balanced appraisal of the film, Star Wars fan Miles Ariely admitted Thursday that an online publication’s middling review of The Rise Of Skywalker had left him on the fence about whether he would still threaten to kill the critic who wrote it. “I’m really of two minds about this, because on the one hand, he said the new movie fails to live up to the original trilogy, which makes me at least want to throw a brick through his window with a note telling him to watch his back,” said Ariely, confirming he had already drafted an eight-page-long death threat to Stan Corimer of the website Screen-On Time, but had not yet decided whether to post it to the reviewer’s Facebook page. “On the other hand, though, he commended J.J. Abrams’ skillful pacing and faithfulness to George Lucas’ vision, which makes me wonder if I should just call the whole thing off. Now, I really don’t feel like camping outside his house for hours. Maybe I could go with a response that’s somewhere in between, like, threatening to kill his dog but not everyone in his whole family? I don’t know. This is a tough one.” At press time, sources reported that Ariely had resolved to wear his Ewok costume while he murdered the critic in his sleep.&quot;</span><span class="p">]}</span>
<span class="n">example_prediction</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">classify</span><span class="p">(</span><span class="n">tc</span><span class="o">.</span><span class="n">SFrame</span><span class="p">(</span><span class="n">example_text</span><span class="p">))</span>
<span class="k">print</span><span class="p">(</span><span class="n">example_prediction</span><span class="p">,</span> <span class="n">flush</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="o">+-------+--------------------+</span>
<span class="o">|</span> <span class="k">class</span> <span class="err">|    </span><span class="nc">probability</span>     <span class="o">|</span>
<span class="o">+-------+--------------------+</span>
<span class="o">|</span>  <span class="n">FAKE</span> <span class="o">|</span> <span class="mf">0.9245648658345308</span> <span class="o">|</span>
<span class="o">+-------+--------------------+</span>
<span class="p">[</span><span class="mi">1</span> <span class="n">rows</span> <span class="n">x</span> <span class="mi">2</span> <span class="n">columns</span><span class="p">]</span>
</div>

</code></pre><h3>Exporting the Model</h3><pre><code><div class="highlight"><span></span><span class="n">model_name</span> <span class="o">=</span> <span class="s1">&#39;FakeNews&#39;</span>
<span class="n">coreml_model_name</span> <span class="o">=</span> <span class="n">model_name</span> <span class="o">+</span> <span class="s1">&#39;.mlmodel&#39;</span>
<span class="n">exportedModel</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">export_coreml</span><span class="p">(</span><span class="n">coreml_model_name</span><span class="p">)</span>
</div>

</code></pre><p><strong>Note: To download files from Google Volab, simply click on the files section in the sidebar, right click on filename and then click on downlaod</strong></p><p><a href="https://colab.research.google.com/drive/1onMXGkhA__X2aOFdsoVL-6HQBsWQhOP4">Link to Colab Notebook</a></p><h2>Building the App using SwiftUI</h2><h3>Initial Setup</h3><p>First we create a single view app (make sure you check the use SwiftUI button)</p><p>Then we copy our .mlmodel file to our project (Just drag and drop the file in the XCode Files Sidebar)</p><p>Our ML Model does not take a string directly as an input, rather it takes bag of words as an input. DescriptionThe bag-of-words model is a simplifying representation used in NLP, in this text is represented as a bag of words, without any regatd of grammar or order, but noting multiplicity</p><p>We define our bag of words function</p><pre><code><div class="highlight"><span></span><span class="kd">func</span> <span class="nf">bow</span><span class="p">(</span><span class="n">text</span><span class="p">:</span> <span class="nb">String</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="p">[</span><span class="nb">String</span><span class="p">:</span> <span class="nb">Double</span><span class="p">]</span> <span class="p">{</span>
        <span class="kd">var</span> <span class="nv">bagOfWords</span> <span class="p">=</span> <span class="p">[</span><span class="nb">String</span><span class="p">:</span> <span class="nb">Double</span><span class="p">]()</span>
        
        <span class="kd">let</span> <span class="nv">tagger</span> <span class="p">=</span> <span class="bp">NSLinguisticTagger</span><span class="p">(</span><span class="n">tagSchemes</span><span class="p">:</span> <span class="p">[.</span><span class="n">tokenType</span><span class="p">],</span> <span class="n">options</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span>
        <span class="kd">let</span> <span class="nv">range</span> <span class="p">=</span> <span class="n">NSRange</span><span class="p">(</span><span class="n">location</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">length</span><span class="p">:</span> <span class="n">text</span><span class="p">.</span><span class="n">utf16</span><span class="p">.</span><span class="bp">count</span><span class="p">)</span>
        <span class="kd">let</span> <span class="nv">options</span><span class="p">:</span> <span class="bp">NSLinguisticTagger</span><span class="p">.</span><span class="n">Options</span> <span class="p">=</span> <span class="p">[.</span><span class="n">omitPunctuation</span><span class="p">,</span> <span class="p">.</span><span class="n">omitWhitespace</span><span class="p">]</span>
        <span class="n">tagger</span><span class="p">.</span><span class="n">string</span> <span class="p">=</span> <span class="n">text</span>
        
        <span class="n">tagger</span><span class="p">.</span><span class="n">enumerateTags</span><span class="p">(</span><span class="k">in</span><span class="p">:</span> <span class="n">range</span><span class="p">,</span> <span class="n">unit</span><span class="p">:</span> <span class="p">.</span><span class="n">word</span><span class="p">,</span> <span class="n">scheme</span><span class="p">:</span> <span class="p">.</span><span class="n">tokenType</span><span class="p">,</span> <span class="n">options</span><span class="p">:</span> <span class="n">options</span><span class="p">)</span> <span class="p">{</span> <span class="kc">_</span><span class="p">,</span> <span class="n">tokenRange</span><span class="p">,</span> <span class="kc">_</span> <span class="k">in</span>
            <span class="kd">let</span> <span class="nv">word</span> <span class="p">=</span> <span class="p">(</span><span class="n">text</span> <span class="k">as</span> <span class="bp">NSString</span><span class="p">).</span><span class="n">substring</span><span class="p">(</span><span class="n">with</span><span class="p">:</span> <span class="n">tokenRange</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">bagOfWords</span><span class="p">[</span><span class="n">word</span><span class="p">]</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
                <span class="n">bagOfWords</span><span class="p">[</span><span class="n">word</span><span class="p">]</span><span class="o">!</span> <span class="o">+=</span> <span class="mi">1</span>
            <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
                <span class="n">bagOfWords</span><span class="p">[</span><span class="n">word</span><span class="p">]</span> <span class="p">=</span> <span class="mi">1</span>
            <span class="p">}</span>
        <span class="p">}</span>
        
        <span class="k">return</span> <span class="n">bagOfWords</span>
    <span class="p">}</span>
</div>

</code></pre><p>We also declare our variables</p><pre><code><div class="highlight"><span></span><span class="p">@</span><span class="n">State</span> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">title</span><span class="p">:</span> <span class="nb">String</span> <span class="p">=</span> <span class="s">&quot;&quot;</span>
<span class="p">@</span><span class="n">State</span> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">headline</span><span class="p">:</span> <span class="nb">String</span> <span class="p">=</span> <span class="s">&quot;&quot;</span>
<span class="p">@</span><span class="n">State</span> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">alertTitle</span> <span class="p">=</span> <span class="s">&quot;&quot;</span>
<span class="p">@</span><span class="n">State</span> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">alertText</span> <span class="p">=</span> <span class="s">&quot;&quot;</span>
<span class="p">@</span><span class="n">State</span> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">showingAlert</span> <span class="p">=</span> <span class="kc">false</span>
</div>

</code></pre><p>Finally, we implement a simple function which reads the two text fields, creates their bag of words representation and displays an alert with the appropriate result</p><p><strong>Complete Code</strong></p><pre><code><div class="highlight"><span></span><span class="kd">import</span> <span class="nc">SwiftUI</span>

<span class="kd">struct</span> <span class="nc">ContentView</span><span class="p">:</span> <span class="n">View</span> <span class="p">{</span>
    <span class="p">@</span><span class="n">State</span> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">title</span><span class="p">:</span> <span class="nb">String</span> <span class="p">=</span> <span class="s">&quot;&quot;</span>
    <span class="p">@</span><span class="n">State</span> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">headline</span><span class="p">:</span> <span class="nb">String</span> <span class="p">=</span> <span class="s">&quot;&quot;</span>
    
    <span class="p">@</span><span class="n">State</span> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">alertTitle</span> <span class="p">=</span> <span class="s">&quot;&quot;</span>
    <span class="p">@</span><span class="n">State</span> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">alertText</span> <span class="p">=</span> <span class="s">&quot;&quot;</span>
    <span class="p">@</span><span class="n">State</span> <span class="kd">private</span> <span class="kd">var</span> <span class="nv">showingAlert</span> <span class="p">=</span> <span class="kc">false</span>
    
    <span class="kd">var</span> <span class="nv">body</span><span class="p">:</span> <span class="n">some</span> <span class="n">View</span> <span class="p">{</span>
        <span class="n">NavigationView</span> <span class="p">{</span>
            <span class="n">VStack</span><span class="p">(</span><span class="n">alignment</span><span class="p">:</span> <span class="p">.</span><span class="n">leading</span><span class="p">)</span> <span class="p">{</span>
                <span class="n">Text</span><span class="p">(</span><span class="s">&quot;Headline&quot;</span><span class="p">).</span><span class="n">font</span><span class="p">(.</span><span class="n">headline</span><span class="p">)</span>
                <span class="n">TextField</span><span class="p">(</span><span class="s">&quot;Please Enter Headline&quot;</span><span class="p">,</span> <span class="n">text</span><span class="p">:</span> <span class="err">$</span><span class="n">title</span><span class="p">)</span>
                    <span class="p">.</span><span class="n">lineLimit</span><span class="p">(</span><span class="kc">nil</span><span class="p">)</span>
                <span class="n">Text</span><span class="p">(</span><span class="s">&quot;Body&quot;</span><span class="p">).</span><span class="n">font</span><span class="p">(.</span><span class="n">headline</span><span class="p">)</span>
                <span class="n">TextField</span><span class="p">(</span><span class="s">&quot;Please Enter the content&quot;</span><span class="p">,</span> <span class="n">text</span><span class="p">:</span> <span class="err">$</span><span class="n">headline</span><span class="p">)</span>
                <span class="p">.</span><span class="n">lineLimit</span><span class="p">(</span><span class="kc">nil</span><span class="p">)</span>
            <span class="p">}</span>
                <span class="p">.</span><span class="n">navigationBarTitle</span><span class="p">(</span><span class="s">&quot;Fake News Checker&quot;</span><span class="p">)</span>
            <span class="p">.</span><span class="n">navigationBarItems</span><span class="p">(</span><span class="n">trailing</span><span class="p">:</span>
                <span class="n">Button</span><span class="p">(</span><span class="n">action</span><span class="p">:</span> <span class="n">classifyFakeNews</span><span class="p">)</span> <span class="p">{</span>
                    <span class="n">Text</span><span class="p">(</span><span class="s">&quot;Check&quot;</span><span class="p">)</span>
                <span class="p">})</span>
            <span class="p">.</span><span class="n">padding</span><span class="p">()</span>
                <span class="p">.</span><span class="n">alert</span><span class="p">(</span><span class="n">isPresented</span><span class="p">:</span> <span class="err">$</span><span class="n">showingAlert</span><span class="p">){</span>
                    <span class="n">Alert</span><span class="p">(</span><span class="n">title</span><span class="p">:</span> <span class="n">Text</span><span class="p">(</span><span class="n">alertTitle</span><span class="p">),</span> <span class="n">message</span><span class="p">:</span> <span class="n">Text</span><span class="p">(</span><span class="n">alertText</span><span class="p">),</span> <span class="n">dismissButton</span><span class="p">:</span> <span class="p">.</span><span class="k">default</span><span class="p">(</span><span class="n">Text</span><span class="p">(</span><span class="s">&quot;OK&quot;</span><span class="p">)))</span>
            <span class="p">}</span>
        <span class="p">}</span>
        
    <span class="p">}</span>
    
    <span class="kd">func</span> <span class="nf">classifyFakeNews</span><span class="p">(){</span>
        <span class="kd">let</span> <span class="nv">model</span> <span class="p">=</span> <span class="n">FakeNews</span><span class="p">()</span>
        <span class="kd">let</span> <span class="nv">myTitle</span> <span class="p">=</span> <span class="n">bow</span><span class="p">(</span><span class="n">text</span><span class="p">:</span> <span class="n">title</span><span class="p">)</span>
        <span class="kd">let</span> <span class="nv">myText</span> <span class="p">=</span> <span class="n">bow</span><span class="p">(</span><span class="n">text</span><span class="p">:</span> <span class="n">headline</span><span class="p">)</span>
        <span class="k">do</span> <span class="p">{</span>
            <span class="kd">let</span> <span class="nv">prediction</span> <span class="p">=</span> <span class="k">try</span> <span class="n">model</span><span class="p">.</span><span class="n">prediction</span><span class="p">(</span><span class="n">title</span><span class="p">:</span> <span class="n">myTitle</span><span class="p">,</span> <span class="n">text</span><span class="p">:</span> <span class="n">myText</span><span class="p">)</span>
            <span class="n">alertTitle</span> <span class="p">=</span> <span class="n">prediction</span><span class="p">.</span><span class="n">label</span>
            <span class="n">alertText</span> <span class="p">=</span> <span class="s">&quot;It is likely that this piece of news is </span><span class="si">\(</span><span class="n">prediction</span><span class="p">.</span><span class="n">label</span><span class="p">.</span><span class="n">lowercased</span><span class="si">())</span><span class="s">.&quot;</span>
            <span class="bp">print</span><span class="p">(</span><span class="n">alertText</span><span class="p">)</span>
        <span class="p">}</span> <span class="k">catch</span> <span class="p">{</span>
            <span class="n">alertTitle</span> <span class="p">=</span> <span class="s">&quot;Error&quot;</span>
            <span class="n">alertText</span> <span class="p">=</span> <span class="s">&quot;Sorry, could not classify if the input news was fake or not.&quot;</span>
        <span class="p">}</span>
        
        <span class="n">showingAlert</span> <span class="p">=</span> <span class="kc">true</span>
    <span class="p">}</span>
    <span class="kd">func</span> <span class="nf">bow</span><span class="p">(</span><span class="n">text</span><span class="p">:</span> <span class="nb">String</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="p">[</span><span class="nb">String</span><span class="p">:</span> <span class="nb">Double</span><span class="p">]</span> <span class="p">{</span>
        <span class="kd">var</span> <span class="nv">bagOfWords</span> <span class="p">=</span> <span class="p">[</span><span class="nb">String</span><span class="p">:</span> <span class="nb">Double</span><span class="p">]()</span>
        
        <span class="kd">let</span> <span class="nv">tagger</span> <span class="p">=</span> <span class="bp">NSLinguisticTagger</span><span class="p">(</span><span class="n">tagSchemes</span><span class="p">:</span> <span class="p">[.</span><span class="n">tokenType</span><span class="p">],</span> <span class="n">options</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span>
        <span class="kd">let</span> <span class="nv">range</span> <span class="p">=</span> <span class="n">NSRange</span><span class="p">(</span><span class="n">location</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">length</span><span class="p">:</span> <span class="n">text</span><span class="p">.</span><span class="n">utf16</span><span class="p">.</span><span class="bp">count</span><span class="p">)</span>
        <span class="kd">let</span> <span class="nv">options</span><span class="p">:</span> <span class="bp">NSLinguisticTagger</span><span class="p">.</span><span class="n">Options</span> <span class="p">=</span> <span class="p">[.</span><span class="n">omitPunctuation</span><span class="p">,</span> <span class="p">.</span><span class="n">omitWhitespace</span><span class="p">]</span>
        <span class="n">tagger</span><span class="p">.</span><span class="n">string</span> <span class="p">=</span> <span class="n">text</span>
        
        <span class="n">tagger</span><span class="p">.</span><span class="n">enumerateTags</span><span class="p">(</span><span class="k">in</span><span class="p">:</span> <span class="n">range</span><span class="p">,</span> <span class="n">unit</span><span class="p">:</span> <span class="p">.</span><span class="n">word</span><span class="p">,</span> <span class="n">scheme</span><span class="p">:</span> <span class="p">.</span><span class="n">tokenType</span><span class="p">,</span> <span class="n">options</span><span class="p">:</span> <span class="n">options</span><span class="p">)</span> <span class="p">{</span> <span class="kc">_</span><span class="p">,</span> <span class="n">tokenRange</span><span class="p">,</span> <span class="kc">_</span> <span class="k">in</span>
            <span class="kd">let</span> <span class="nv">word</span> <span class="p">=</span> <span class="p">(</span><span class="n">text</span> <span class="k">as</span> <span class="bp">NSString</span><span class="p">).</span><span class="n">substring</span><span class="p">(</span><span class="n">with</span><span class="p">:</span> <span class="n">tokenRange</span><span class="p">)</span>
            <span class="k">if</span> <span class="n">bagOfWords</span><span class="p">[</span><span class="n">word</span><span class="p">]</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
                <span class="n">bagOfWords</span><span class="p">[</span><span class="n">word</span><span class="p">]</span><span class="o">!</span> <span class="o">+=</span> <span class="mi">1</span>
            <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
                <span class="n">bagOfWords</span><span class="p">[</span><span class="n">word</span><span class="p">]</span> <span class="p">=</span> <span class="mi">1</span>
            <span class="p">}</span>
        <span class="p">}</span>
        
        <span class="k">return</span> <span class="n">bagOfWords</span>
    <span class="p">}</span>
<span class="p">}</span>

<span class="kd">struct</span> <span class="nc">ContentView_Previews</span><span class="p">:</span> <span class="n">PreviewProvider</span> <span class="p">{</span>
    <span class="kd">static</span> <span class="kd">var</span> <span class="nv">previews</span><span class="p">:</span> <span class="n">some</span> <span class="n">View</span> <span class="p">{</span>
        <span class="n">ContentView</span><span class="p">()</span>
    <span class="p">}</span>
<span class="p">}</span>
</div>

</code></pre>]]></content:encoded></item><item><guid isPermaLink="true">https://navanchauhan.github.io/posts/2019-12-16-TensorFlow-Polynomial-Regression</guid><title>Polynomial Regression Using TensorFlow</title><description>Polynomial regression using TensorFlow</description><link>https://navanchauhan.github.io/posts/2019-12-16-TensorFlow-Polynomial-Regression</link><pubDate>Mon, 16 Dec 2019 14:16:00 +0530</pubDate><content:encoded><![CDATA[<h1>Polynomial Regression Using TensorFlow</h1><p><strong>In this tutorial you will learn about polynomial regression and how you can implement it in Tensorflow.</strong></p><p>In this, we will be performing polynomial regression using 5 types of equations -</p><ul><li>Linear</li><li>Quadratic</li><li>Cubic</li><li>Quartic</li><li>Quintic</li></ul><h2>Regression</h2><h3>What is Regression?</h3><p>Regression is a statistical measurement that is used to try to determine the relationship between a dependent variable (often denoted by Y), and series of varying variables (called independent variables, often denoted by X ).</p><h3>What is Polynomial Regression</h3><p>This is a form of Regression Analysis where the relationship between Y and X is denoted as the nth degree/power of X. Polynomial regression even fits a non-linear relationship (e.g when the points don't form a straight line).</p><h2>Imports</h2><pre><code><div class="highlight"><span></span><span class="kn">import</span> <span class="nn">tensorflow.compat.v1</span> <span class="kn">as</span> <span class="nn">tf</span>
<span class="n">tf</span><span class="o">.</span><span class="n">disable_v2_behavior</span><span class="p">()</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
</div>

</code></pre><h2>Dataset</h2><h3>Creating Random Data</h3><p>Even though in this tutorial we will use a Position Vs Salary datasset, it is important to know how to create synthetic data</p><p>To create 50 values spaced evenly between 0 and 50, we use NumPy's linspace funtion</p><p><code>linspace(lower_limit, upper_limit, no_of_observations)</code></p><pre><code><div class="highlight"><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">50</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">50</span><span class="p">)</span>
</div>

</code></pre><p>We use the following function to add noise to the data, so that our values</p><pre><code><div class="highlight"><span></span><span class="n">x</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">50</span><span class="p">)</span>
<span class="n">y</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">50</span><span class="p">)</span>
</div>

</code></pre><h3>Position vs Salary Dataset</h3><p>We will be using https://drive.google.com/file/d/1tNL4jxZEfpaP4oflfSn6pIHJX7Pachm9/view (Salary vs Position Dataset)</p><pre><code><div class="highlight"><span></span><span class="nt">!wget</span><span class="na"> --no-check-certificate &#39;https</span><span class="p">:</span><span class="nc">//docs.google.com/uc?export</span><span class="o">=</span><span class="l">download&amp;id=1tNL4jxZEfpaP4oflfSn6pIHJX7Pachm9&#39; -O data.csv</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s2">&quot;data.csv&quot;</span><span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">df</span> <span class="c1"># this gives us a preview of the dataset we are working with</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="o">|</span> <span class="n">Position</span>          <span class="o">|</span> <span class="n">Level</span> <span class="o">|</span> <span class="n">Salary</span>  <span class="o">|</span>
<span class="o">|-------------------|-------|---------|</span>
<span class="o">|</span> <span class="n">Business</span> <span class="n">Analyst</span>  <span class="o">|</span> <span class="mi">1</span>     <span class="o">|</span> <span class="mi">45000</span>   <span class="o">|</span>
<span class="o">|</span> <span class="n">Junior</span> <span class="n">Consultant</span> <span class="o">|</span> <span class="mi">2</span>     <span class="o">|</span> <span class="mi">50000</span>   <span class="o">|</span>
<span class="o">|</span> <span class="n">Senior</span> <span class="n">Consultant</span> <span class="o">|</span> <span class="mi">3</span>     <span class="o">|</span> <span class="mi">60000</span>   <span class="o">|</span>
<span class="o">|</span> <span class="n">Manager</span>           <span class="o">|</span> <span class="mi">4</span>     <span class="o">|</span> <span class="mi">80000</span>   <span class="o">|</span>
<span class="o">|</span> <span class="n">Country</span> <span class="n">Manager</span>   <span class="o">|</span> <span class="mi">5</span>     <span class="o">|</span> <span class="mi">110000</span>  <span class="o">|</span>
<span class="o">|</span> <span class="n">Region</span> <span class="n">Manager</span>    <span class="o">|</span> <span class="mi">6</span>     <span class="o">|</span> <span class="mi">150000</span>  <span class="o">|</span>
<span class="o">|</span> <span class="n">Partner</span>           <span class="o">|</span> <span class="mi">7</span>     <span class="o">|</span> <span class="mi">200000</span>  <span class="o">|</span>
<span class="o">|</span> <span class="n">Senior</span> <span class="n">Partner</span>    <span class="o">|</span> <span class="mi">8</span>     <span class="o">|</span> <span class="mi">300000</span>  <span class="o">|</span>
<span class="o">|</span> <span class="n">C</span><span class="o">-</span><span class="n">level</span>           <span class="o">|</span> <span class="mi">9</span>     <span class="o">|</span> <span class="mi">500000</span>  <span class="o">|</span>
<span class="o">|</span> <span class="n">CEO</span>               <span class="o">|</span> <span class="mi">10</span>    <span class="o">|</span> <span class="mi">1000000</span> <span class="o">|</span>
</div>

</code></pre><p>We convert the salary column as the ordinate (y-cordinate) and level column as the abscissa</p><pre><code><div class="highlight"><span></span><span class="n">abscissa</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Level&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">to_list</span><span class="p">()</span> <span class="c1"># abscissa = [1,2,3,4,5,6,7,8,9,10]</span>
<span class="n">ordinate</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Salary&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">to_list</span><span class="p">()</span> <span class="c1"># ordinate = [45000,50000,60000,80000,110000,150000,200000,300000,500000,1000000]</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">abscissa</span><span class="p">)</span> <span class="c1"># no of observations</span>
<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">ordinate</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Salary&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Position&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Salary vs Position&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</div>

</code></pre><img src="https://navanchauhan.github.io//assets/gciTales/03-regression/1.png"/><h2>Defining Stuff</h2><pre><code><div class="highlight"><span></span><span class="n">X</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">placeholder</span><span class="p">(</span><span class="s2">&quot;float&quot;</span><span class="p">)</span>
<span class="n">Y</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">placeholder</span><span class="p">(</span><span class="s2">&quot;float&quot;</span><span class="p">)</span>
</div>

</code></pre><h3>Defining Variables</h3><p>We first define all the coefficients and constant as tensorflow variables haveing a random intitial value</p><pre><code><div class="highlight"><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(),</span> <span class="n">name</span> <span class="o">=</span> <span class="s2">&quot;a&quot;</span><span class="p">)</span>
<span class="n">b</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(),</span> <span class="n">name</span> <span class="o">=</span> <span class="s2">&quot;b&quot;</span><span class="p">)</span>
<span class="n">c</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(),</span> <span class="n">name</span> <span class="o">=</span> <span class="s2">&quot;c&quot;</span><span class="p">)</span>
<span class="n">d</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(),</span> <span class="n">name</span> <span class="o">=</span> <span class="s2">&quot;d&quot;</span><span class="p">)</span>
<span class="n">e</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(),</span> <span class="n">name</span> <span class="o">=</span> <span class="s2">&quot;e&quot;</span><span class="p">)</span>
<span class="n">f</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(),</span> <span class="n">name</span> <span class="o">=</span> <span class="s2">&quot;f&quot;</span><span class="p">)</span>
</div>

</code></pre><h3>Model Configuration</h3><pre><code><div class="highlight"><span></span><span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">0.2</span>
<span class="n">no_of_epochs</span> <span class="o">=</span> <span class="mi">25000</span>
</div>

</code></pre><h3>Equations</h3><pre><code><div class="highlight"><span></span><span class="n">deg1</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">X</span> <span class="o">+</span> <span class="n">b</span>
<span class="n">deg2</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">b</span><span class="o">*</span><span class="n">X</span> <span class="o">+</span> <span class="n">c</span>
<span class="n">deg3</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span> <span class="o">+</span> <span class="n">b</span><span class="o">*</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span><span class="o">*</span><span class="n">X</span> <span class="o">+</span> <span class="n">d</span>
<span class="n">deg4</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span> <span class="o">+</span> <span class="n">b</span><span class="o">*</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span><span class="o">*</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">d</span><span class="o">*</span><span class="n">X</span> <span class="o">+</span> <span class="n">e</span>
<span class="n">deg5</span> <span class="o">=</span> <span class="n">a</span><span class="o">*</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span> <span class="o">+</span> <span class="n">b</span><span class="o">*</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span> <span class="o">+</span> <span class="n">c</span><span class="o">*</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span> <span class="o">+</span> <span class="n">d</span><span class="o">*</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">e</span><span class="o">*</span><span class="n">X</span> <span class="o">+</span> <span class="n">f</span>
</div>

</code></pre><h3>Cost Function</h3><p>We use the Mean Squared Error Function</p><pre><code><div class="highlight"><span></span><span class="n">mse1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_sum</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">deg1</span><span class="o">-</span><span class="n">Y</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">n</span><span class="p">)</span>
<span class="n">mse2</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_sum</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">deg2</span><span class="o">-</span><span class="n">Y</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">n</span><span class="p">)</span>
<span class="n">mse3</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_sum</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">deg3</span><span class="o">-</span><span class="n">Y</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">n</span><span class="p">)</span>
<span class="n">mse4</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_sum</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">deg4</span><span class="o">-</span><span class="n">Y</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">n</span><span class="p">)</span>
<span class="n">mse5</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_sum</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="n">deg5</span><span class="o">-</span><span class="n">Y</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span><span class="o">/</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">n</span><span class="p">)</span>
</div>

</code></pre><h3>Optimizer</h3><p>We use the AdamOptimizer for the polynomial functions and GradientDescentOptimizer for the linear function</p><pre><code><div class="highlight"><span></span><span class="n">optimizer1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">train</span><span class="o">.</span><span class="n">GradientDescentOptimizer</span><span class="p">(</span><span class="n">learning_rate</span><span class="p">)</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">mse1</span><span class="p">)</span>
<span class="n">optimizer2</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">train</span><span class="o">.</span><span class="n">AdamOptimizer</span><span class="p">(</span><span class="n">learning_rate</span><span class="p">)</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">mse2</span><span class="p">)</span>
<span class="n">optimizer3</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">train</span><span class="o">.</span><span class="n">AdamOptimizer</span><span class="p">(</span><span class="n">learning_rate</span><span class="p">)</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">mse3</span><span class="p">)</span>
<span class="n">optimizer4</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">train</span><span class="o">.</span><span class="n">AdamOptimizer</span><span class="p">(</span><span class="n">learning_rate</span><span class="p">)</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">mse4</span><span class="p">)</span>
<span class="n">optimizer5</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">train</span><span class="o">.</span><span class="n">AdamOptimizer</span><span class="p">(</span><span class="n">learning_rate</span><span class="p">)</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">mse5</span><span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">init</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">global_variables_initializer</span><span class="p">()</span>
</div>

</code></pre><h2>Model Predictions</h2><p>For each type of equation first we make the model predict the values of the coefficient(s) and constant, once we get these values we use it to predict the Y values using the X values. We then plot it to compare the actual data and predicted line.</p><h3>Linear Equation</h3><pre><code><div class="highlight"><span></span><span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">Session</span><span class="p">()</span> <span class="k">as</span> <span class="n">sess</span><span class="p">:</span>
    <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">init</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">no_of_epochs</span><span class="p">):</span>
      <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">ordinate</span><span class="p">):</span>
        <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">optimizer1</span><span class="p">,</span> <span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">x</span><span class="p">,</span> <span class="n">Y</span><span class="p">:</span><span class="n">y</span><span class="p">})</span>
      <span class="k">if</span> <span class="p">(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">%</span><span class="mi">1000</span><span class="o">==</span><span class="mi">0</span><span class="p">:</span>
        <span class="n">cost</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">mse1</span><span class="p">,</span><span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">abscissa</span><span class="p">,</span><span class="n">Y</span><span class="p">:</span><span class="n">ordinate</span><span class="p">})</span>
        <span class="k">print</span><span class="p">(</span><span class="s2">&quot;Epoch&quot;</span><span class="p">,(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span> <span class="s2">&quot;: Training Cost:&quot;</span><span class="p">,</span> <span class="n">cost</span><span class="p">,</span><span class="s2">&quot; a,b:&quot;</span><span class="p">,</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">a</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">b</span><span class="p">))</span>

        <span class="n">training_cost</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">mse1</span><span class="p">,</span><span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">abscissa</span><span class="p">,</span><span class="n">Y</span><span class="p">:</span><span class="n">ordinate</span><span class="p">})</span>
        <span class="n">coefficient1</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
        <span class="n">constant</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>

<span class="k">print</span><span class="p">(</span><span class="n">training_cost</span><span class="p">,</span> <span class="n">coefficient1</span><span class="p">,</span> <span class="n">constant</span><span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="nt">Epoch</span><span class="na"> 1000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 2000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 3000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 4000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 5000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 6000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 7000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 8000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 9000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 10000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 11000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 12000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 13000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 14000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 15000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 16000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 17000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 18000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 19000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 20000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 21000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 22000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 23000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 24000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">Epoch</span><span class="na"> 25000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">88999125000.0</span><span class="err">  </span><span class="nc">a,b</span><span class="p">:</span><span class="err"> </span><span class="nc">180396.42</span><span class="err"> </span><span class="nc">-478869.12</span>
<span class="nt">88999125000.0</span><span class="na"> 180396.42 -478869.12</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">predictions</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">abscissa</span><span class="p">:</span>
  <span class="n">predictions</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">coefficient1</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">constant</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">abscissa</span> <span class="p">,</span> <span class="n">ordinate</span><span class="p">,</span> <span class="s1">&#39;ro&#39;</span><span class="p">,</span> <span class="n">label</span> <span class="o">=</span><span class="s1">&#39;Original data&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">predictions</span><span class="p">,</span> <span class="n">label</span> <span class="o">=</span><span class="s1">&#39;Fitted line&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Linear Regression Result&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</div>

</code></pre><img src="https://navanchauhan.github.io//assets/gciTales/03-regression/2.png"/><h3>Quadratic Equation</h3><pre><code><div class="highlight"><span></span><span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">Session</span><span class="p">()</span> <span class="k">as</span> <span class="n">sess</span><span class="p">:</span>
    <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">init</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">no_of_epochs</span><span class="p">):</span>
      <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">ordinate</span><span class="p">):</span>
        <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">optimizer2</span><span class="p">,</span> <span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">x</span><span class="p">,</span> <span class="n">Y</span><span class="p">:</span><span class="n">y</span><span class="p">})</span>
      <span class="k">if</span> <span class="p">(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">%</span><span class="mi">1000</span><span class="o">==</span><span class="mi">0</span><span class="p">:</span>
        <span class="n">cost</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">mse2</span><span class="p">,</span><span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">abscissa</span><span class="p">,</span><span class="n">Y</span><span class="p">:</span><span class="n">ordinate</span><span class="p">})</span>
        <span class="k">print</span><span class="p">(</span><span class="s2">&quot;Epoch&quot;</span><span class="p">,(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span> <span class="s2">&quot;: Training Cost:&quot;</span><span class="p">,</span> <span class="n">cost</span><span class="p">,</span><span class="s2">&quot; a,b,c:&quot;</span><span class="p">,</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">a</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">b</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">c</span><span class="p">))</span>

        <span class="n">training_cost</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">mse2</span><span class="p">,</span><span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">abscissa</span><span class="p">,</span><span class="n">Y</span><span class="p">:</span><span class="n">ordinate</span><span class="p">})</span>
        <span class="n">coefficient1</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
        <span class="n">coefficient2</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
        <span class="n">constant</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>

<span class="k">print</span><span class="p">(</span><span class="n">training_cost</span><span class="p">,</span> <span class="n">coefficient1</span><span class="p">,</span> <span class="n">coefficient2</span><span class="p">,</span> <span class="n">constant</span><span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="nt">Epoch</span><span class="na"> 1000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">52571360000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">1002.4456</span><span class="err"> </span><span class="nc">1097.0197</span><span class="err"> </span><span class="nc">1276.6921</span>
<span class="nt">Epoch</span><span class="na"> 2000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">37798890000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">1952.4263</span><span class="err"> </span><span class="nc">2130.2825</span><span class="err"> </span><span class="nc">2469.7756</span>
<span class="nt">Epoch</span><span class="na"> 3000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">26751185000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">2839.5825</span><span class="err"> </span><span class="nc">3081.6118</span><span class="err"> </span><span class="nc">3554.351</span>
<span class="nt">Epoch</span><span class="na"> 4000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">19020106000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">3644.56</span><span class="err"> </span><span class="nc">3922.9563</span><span class="err"> </span><span class="nc">4486.3135</span>
<span class="nt">Epoch</span><span class="na"> 5000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">14060446000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">4345.042</span><span class="err"> </span><span class="nc">4621.4233</span><span class="err"> </span><span class="nc">5212.693</span>
<span class="nt">Epoch</span><span class="na"> 6000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">11201084000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">4921.1855</span><span class="err"> </span><span class="nc">5148.1504</span><span class="err"> </span><span class="nc">5689.0713</span>
<span class="nt">Epoch</span><span class="na"> 7000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">9732740000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">5364.764</span><span class="err"> </span><span class="nc">5493.0156</span><span class="err"> </span><span class="nc">5906.754</span>
<span class="nt">Epoch</span><span class="na"> 8000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">9050918000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">5685.4067</span><span class="err"> </span><span class="nc">5673.182</span><span class="err"> </span><span class="nc">5902.0728</span>
<span class="nt">Epoch</span><span class="na"> 9000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8750394000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">5906.9814</span><span class="err"> </span><span class="nc">5724.8906</span><span class="err"> </span><span class="nc">5734.746</span>
<span class="nt">Epoch</span><span class="na"> 10000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8613128000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6057.3677</span><span class="err"> </span><span class="nc">5687.3364</span><span class="err"> </span><span class="nc">5461.167</span>
<span class="nt">Epoch</span><span class="na"> 11000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8540034600.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6160.547</span><span class="err"> </span><span class="nc">5592.3022</span><span class="err"> </span><span class="nc">5122.8633</span>
<span class="nt">Epoch</span><span class="na"> 12000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8490983000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6233.9175</span><span class="err"> </span><span class="nc">5462.025</span><span class="err"> </span><span class="nc">4747.111</span>
<span class="nt">Epoch</span><span class="na"> 13000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8450816500.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6289.048</span><span class="err"> </span><span class="nc">5310.7583</span><span class="err"> </span><span class="nc">4350.6997</span>
<span class="nt">Epoch</span><span class="na"> 14000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8414082000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6333.199</span><span class="err"> </span><span class="nc">5147.394</span><span class="err"> </span><span class="nc">3943.9294</span>
<span class="nt">Epoch</span><span class="na"> 15000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8378841600.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6370.7944</span><span class="err"> </span><span class="nc">4977.1704</span><span class="err"> </span><span class="nc">3532.476</span>
<span class="nt">Epoch</span><span class="na"> 16000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8344471000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6404.468</span><span class="err"> </span><span class="nc">4803.542</span><span class="err"> </span><span class="nc">3120.2087</span>
<span class="nt">Epoch</span><span class="na"> 17000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8310785500.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6435.365</span><span class="err"> </span><span class="nc">4628.1523</span><span class="err"> </span><span class="nc">2709.1445</span>
<span class="nt">Epoch</span><span class="na"> 18000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8277482000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6465.5493</span><span class="err"> </span><span class="nc">4451.833</span><span class="err"> </span><span class="nc">2300.2783</span>
<span class="nt">Epoch</span><span class="na"> 19000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8244650000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6494.609</span><span class="err"> </span><span class="nc">4274.826</span><span class="err"> </span><span class="nc">1894.3738</span>
<span class="nt">Epoch</span><span class="na"> 20000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8212349000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6522.8247</span><span class="err"> </span><span class="nc">4098.1733</span><span class="err"> </span><span class="nc">1491.9915</span>
<span class="nt">Epoch</span><span class="na"> 21000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8180598300.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6550.6567</span><span class="err"> </span><span class="nc">3922.7405</span><span class="err"> </span><span class="nc">1093.3868</span>
<span class="nt">Epoch</span><span class="na"> 22000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8149257700.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6578.489</span><span class="err"> </span><span class="nc">3747.8362</span><span class="err"> </span><span class="nc">698.53357</span>
<span class="nt">Epoch</span><span class="na"> 23000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8118325000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6606.1973</span><span class="err"> </span><span class="nc">3573.2742</span><span class="err"> </span><span class="nc">307.3541</span>
<span class="nt">Epoch</span><span class="na"> 24000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8088001000.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6632.96</span><span class="err"> </span><span class="nc">3399.878</span><span class="err"> </span><span class="nc">-79.89219</span>
<span class="nt">Epoch</span><span class="na"> 25000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">8058094600.0</span><span class="err">  </span><span class="nc">a,b,c</span><span class="p">:</span><span class="err"> </span><span class="nc">6659.793</span><span class="err"> </span><span class="nc">3227.2517</span><span class="err"> </span><span class="nc">-463.03156</span>
<span class="nt">8058094600.0</span><span class="na"> 6659.793 3227.2517 -463.03156</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">predictions</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">abscissa</span><span class="p">:</span>
  <span class="n">predictions</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">coefficient1</span><span class="o">*</span><span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">coefficient2</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">constant</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">abscissa</span> <span class="p">,</span> <span class="n">ordinate</span><span class="p">,</span> <span class="s1">&#39;ro&#39;</span><span class="p">,</span> <span class="n">label</span> <span class="o">=</span><span class="s1">&#39;Original data&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">predictions</span><span class="p">,</span> <span class="n">label</span> <span class="o">=</span><span class="s1">&#39;Fitted line&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Quadratic Regression Result&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</div>

</code></pre><img src="https://navanchauhan.github.io//assets/gciTales/03-regression/3.png"/><h3>Cubic</h3><pre><code><div class="highlight"><span></span><span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">Session</span><span class="p">()</span> <span class="k">as</span> <span class="n">sess</span><span class="p">:</span>
    <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">init</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">no_of_epochs</span><span class="p">):</span>
      <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">ordinate</span><span class="p">):</span>
        <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">optimizer3</span><span class="p">,</span> <span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">x</span><span class="p">,</span> <span class="n">Y</span><span class="p">:</span><span class="n">y</span><span class="p">})</span>
      <span class="k">if</span> <span class="p">(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">%</span><span class="mi">1000</span><span class="o">==</span><span class="mi">0</span><span class="p">:</span>
        <span class="n">cost</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">mse3</span><span class="p">,</span><span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">abscissa</span><span class="p">,</span><span class="n">Y</span><span class="p">:</span><span class="n">ordinate</span><span class="p">})</span>
        <span class="k">print</span><span class="p">(</span><span class="s2">&quot;Epoch&quot;</span><span class="p">,(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span> <span class="s2">&quot;: Training Cost:&quot;</span><span class="p">,</span> <span class="n">cost</span><span class="p">,</span><span class="s2">&quot; a,b,c,d:&quot;</span><span class="p">,</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">a</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">b</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">c</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">d</span><span class="p">))</span>

        <span class="n">training_cost</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">mse3</span><span class="p">,</span><span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">abscissa</span><span class="p">,</span><span class="n">Y</span><span class="p">:</span><span class="n">ordinate</span><span class="p">})</span>
        <span class="n">coefficient1</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
        <span class="n">coefficient2</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
        <span class="n">coefficient3</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
        <span class="n">constant</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>

<span class="k">print</span><span class="p">(</span><span class="n">training_cost</span><span class="p">,</span> <span class="n">coefficient1</span><span class="p">,</span> <span class="n">coefficient2</span><span class="p">,</span> <span class="n">coefficient3</span><span class="p">,</span> <span class="n">constant</span><span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="nt">Epoch</span><span class="na"> 1000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">4279814000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">670.1527</span><span class="err"> </span><span class="nc">694.4212</span><span class="err"> </span><span class="nc">751.4653</span><span class="err"> </span><span class="nc">903.9527</span>
<span class="nt">Epoch</span><span class="na"> 2000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3770950400.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">742.6414</span><span class="err"> </span><span class="nc">666.3489</span><span class="err"> </span><span class="nc">636.94525</span><span class="err"> </span><span class="nc">859.2088</span>
<span class="nt">Epoch</span><span class="na"> 3000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3717708300.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">756.2582</span><span class="err"> </span><span class="nc">569.3339</span><span class="err"> </span><span class="nc">448.105</span><span class="err"> </span><span class="nc">748.23956</span>
<span class="nt">Epoch</span><span class="na"> 4000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3667464000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">769.4476</span><span class="err"> </span><span class="nc">474.0318</span><span class="err"> </span><span class="nc">265.5761</span><span class="err"> </span><span class="nc">654.75525</span>
<span class="nt">Epoch</span><span class="na"> 5000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3620040700.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">782.32324</span><span class="err"> </span><span class="nc">380.54272</span><span class="err"> </span><span class="nc">89.39888</span><span class="err"> </span><span class="nc">578.5136</span>
<span class="nt">Epoch</span><span class="na"> 6000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3575265800.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">794.8898</span><span class="err"> </span><span class="nc">288.83356</span><span class="err"> </span><span class="nc">-80.5215</span><span class="err"> </span><span class="nc">519.13654</span>
<span class="nt">Epoch</span><span class="na"> 7000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3532972000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">807.1608</span><span class="err"> </span><span class="nc">198.87044</span><span class="err"> </span><span class="nc">-244.31102</span><span class="err"> </span><span class="nc">476.2061</span>
<span class="nt">Epoch</span><span class="na"> 8000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3493009200.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">819.13513</span><span class="err"> </span><span class="nc">110.64169</span><span class="err"> </span><span class="nc">-402.0677</span><span class="err"> </span><span class="nc">449.3291</span>
<span class="nt">Epoch</span><span class="na"> 9000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3455228400.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">830.80255</span><span class="err"> </span><span class="nc">24.0964</span><span class="err"> </span><span class="nc">-553.92804</span><span class="err"> </span><span class="nc">438.0652</span>
<span class="nt">Epoch</span><span class="na"> 10000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3419475500.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">842.21594</span><span class="err"> </span><span class="nc">-60.797424</span><span class="err"> </span><span class="nc">-700.0123</span><span class="err"> </span><span class="nc">441.983</span>
<span class="nt">Epoch</span><span class="na"> 11000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3385625300.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">853.3363</span><span class="err"> </span><span class="nc">-144.08699</span><span class="err"> </span><span class="nc">-840.467</span><span class="err"> </span><span class="nc">460.6356</span>
<span class="nt">Epoch</span><span class="na"> 12000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3353544700.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">864.19135</span><span class="err"> </span><span class="nc">-225.8125</span><span class="err"> </span><span class="nc">-975.4196</span><span class="err"> </span><span class="nc">493.57703</span>
<span class="nt">Epoch</span><span class="na"> 13000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3323125000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">874.778</span><span class="err"> </span><span class="nc">-305.98932</span><span class="err"> </span><span class="nc">-1104.9867</span><span class="err"> </span><span class="nc">540.39465</span>
<span class="nt">Epoch</span><span class="na"> 14000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3294257000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">885.1007</span><span class="err"> </span><span class="nc">-384.63474</span><span class="err"> </span><span class="nc">-1229.277</span><span class="err"> </span><span class="nc">600.65607</span>
<span class="nt">Epoch</span><span class="na"> 15000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3266820000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">895.18823</span><span class="err"> </span><span class="nc">-461.819</span><span class="err"> </span><span class="nc">-1348.4417</span><span class="err"> </span><span class="nc">673.9051</span>
<span class="nt">Epoch</span><span class="na"> 16000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3240736000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">905.0128</span><span class="err"> </span><span class="nc">-537.541</span><span class="err"> </span><span class="nc">-1462.6171</span><span class="err"> </span><span class="nc">759.7118</span>
<span class="nt">Epoch</span><span class="na"> 17000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3215895000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">914.60065</span><span class="err"> </span><span class="nc">-611.8676</span><span class="err"> </span><span class="nc">-1571.9058</span><span class="err"> </span><span class="nc">857.6638</span>
<span class="nt">Epoch</span><span class="na"> 18000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3192216800.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">923.9603</span><span class="err"> </span><span class="nc">-684.8093</span><span class="err"> </span><span class="nc">-1676.4642</span><span class="err"> </span><span class="nc">967.30475</span>
<span class="nt">Epoch</span><span class="na"> 19000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3169632300.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">933.08594</span><span class="err"> </span><span class="nc">-756.3582</span><span class="err"> </span><span class="nc">-1776.4275</span><span class="err"> </span><span class="nc">1088.2198</span>
<span class="nt">Epoch</span><span class="na"> 20000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3148046300.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">941.9928</span><span class="err"> </span><span class="nc">-826.6257</span><span class="err"> </span><span class="nc">-1871.9355</span><span class="err"> </span><span class="nc">1219.9702</span>
<span class="nt">Epoch</span><span class="na"> 21000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3127394800.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">950.67896</span><span class="err"> </span><span class="nc">-895.6205</span><span class="err"> </span><span class="nc">-1963.0989</span><span class="err"> </span><span class="nc">1362.1665</span>
<span class="nt">Epoch</span><span class="na"> 22000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3107608600.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">959.1487</span><span class="err"> </span><span class="nc">-963.38116</span><span class="err"> </span><span class="nc">-2050.0586</span><span class="err"> </span><span class="nc">1514.4026</span>
<span class="nt">Epoch</span><span class="na"> 23000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3088618200.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">967.4355</span><span class="err"> </span><span class="nc">-1029.9625</span><span class="err"> </span><span class="nc">-2132.961</span><span class="err"> </span><span class="nc">1676.2717</span>
<span class="nt">Epoch</span><span class="na"> 24000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3070361300.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">975.52875</span><span class="err"> </span><span class="nc">-1095.4292</span><span class="err"> </span><span class="nc">-2211.854</span><span class="err"> </span><span class="nc">1847.4485</span>
<span class="nt">Epoch</span><span class="na"> 25000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">3052791300.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">983.4346</span><span class="err"> </span><span class="nc">-1159.7922</span><span class="err"> </span><span class="nc">-2286.9412</span><span class="err"> </span><span class="nc">2027.4857</span>
<span class="nt">3052791300.0</span><span class="na"> 983.4346 -1159.7922 -2286.9412 2027.4857</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">predictions</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">abscissa</span><span class="p">:</span>
  <span class="n">predictions</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">coefficient1</span><span class="o">*</span><span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span> <span class="o">+</span> <span class="n">coefficient2</span><span class="o">*</span><span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">coefficient3</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">constant</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">abscissa</span> <span class="p">,</span> <span class="n">ordinate</span><span class="p">,</span> <span class="s1">&#39;ro&#39;</span><span class="p">,</span> <span class="n">label</span> <span class="o">=</span><span class="s1">&#39;Original data&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">predictions</span><span class="p">,</span> <span class="n">label</span> <span class="o">=</span><span class="s1">&#39;Fitted line&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Cubic Regression Result&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</div>

</code></pre><img src="https://navanchauhan.github.io//assets/gciTales/03-regression/4.png"/><h3>Quartic</h3><pre><code><div class="highlight"><span></span><span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">Session</span><span class="p">()</span> <span class="k">as</span> <span class="n">sess</span><span class="p">:</span>
    <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">init</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">no_of_epochs</span><span class="p">):</span>
      <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">ordinate</span><span class="p">):</span>
        <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">optimizer4</span><span class="p">,</span> <span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">x</span><span class="p">,</span> <span class="n">Y</span><span class="p">:</span><span class="n">y</span><span class="p">})</span>
      <span class="k">if</span> <span class="p">(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">%</span><span class="mi">1000</span><span class="o">==</span><span class="mi">0</span><span class="p">:</span>
        <span class="n">cost</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">mse4</span><span class="p">,</span><span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">abscissa</span><span class="p">,</span><span class="n">Y</span><span class="p">:</span><span class="n">ordinate</span><span class="p">})</span>
        <span class="k">print</span><span class="p">(</span><span class="s2">&quot;Epoch&quot;</span><span class="p">,(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span> <span class="s2">&quot;: Training Cost:&quot;</span><span class="p">,</span> <span class="n">cost</span><span class="p">,</span><span class="s2">&quot; a,b,c,d:&quot;</span><span class="p">,</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">a</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">b</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">c</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">d</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">e</span><span class="p">))</span>

        <span class="n">training_cost</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">mse4</span><span class="p">,</span><span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">abscissa</span><span class="p">,</span><span class="n">Y</span><span class="p">:</span><span class="n">ordinate</span><span class="p">})</span>
        <span class="n">coefficient1</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
        <span class="n">coefficient2</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
        <span class="n">coefficient3</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
        <span class="n">coefficient4</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
        <span class="n">constant</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>

<span class="k">print</span><span class="p">(</span><span class="n">training_cost</span><span class="p">,</span> <span class="n">coefficient1</span><span class="p">,</span> <span class="n">coefficient2</span><span class="p">,</span> <span class="n">coefficient3</span><span class="p">,</span> <span class="n">coefficient4</span><span class="p">,</span> <span class="n">constant</span><span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="nt">Epoch</span><span class="na"> 1000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1902632600.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">84.48304</span><span class="err"> </span><span class="nc">52.210594</span><span class="err"> </span><span class="nc">54.791424</span><span class="err"> </span><span class="nc">142.51952</span><span class="err"> </span><span class="nc">512.0343</span>
<span class="nt">Epoch</span><span class="na"> 2000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1854316200.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">88.998955</span><span class="err"> </span><span class="nc">13.073557</span><span class="err"> </span><span class="nc">14.276088</span><span class="err"> </span><span class="nc">223.55667</span><span class="err"> </span><span class="nc">1056.4655</span>
<span class="nt">Epoch</span><span class="na"> 3000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1812812400.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">92.9462</span><span class="err"> </span><span class="nc">-22.331177</span><span class="err"> </span><span class="nc">-15.262934</span><span class="err"> </span><span class="nc">327.41858</span><span class="err"> </span><span class="nc">1634.9054</span>
<span class="nt">Epoch</span><span class="na"> 4000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1775716000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">96.42522</span><span class="err"> </span><span class="nc">-54.64535</span><span class="err"> </span><span class="nc">-35.829437</span><span class="err"> </span><span class="nc">449.5028</span><span class="err"> </span><span class="nc">2239.1392</span>
<span class="nt">Epoch</span><span class="na"> 5000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1741494100.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">99.524734</span><span class="err"> </span><span class="nc">-84.43976</span><span class="err"> </span><span class="nc">-49.181057</span><span class="err"> </span><span class="nc">585.85876</span><span class="err"> </span><span class="nc">2862.4915</span>
<span class="nt">Epoch</span><span class="na"> 6000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1709199600.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">102.31984</span><span class="err"> </span><span class="nc">-112.19895</span><span class="err"> </span><span class="nc">-56.808075</span><span class="err"> </span><span class="nc">733.1876</span><span class="err"> </span><span class="nc">3499.6199</span>
<span class="nt">Epoch</span><span class="na"> 7000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1678261800.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">104.87324</span><span class="err"> </span><span class="nc">-138.32709</span><span class="err"> </span><span class="nc">-59.9442</span><span class="err"> </span><span class="nc">888.79626</span><span class="err"> </span><span class="nc">4146.2944</span>
<span class="nt">Epoch</span><span class="na"> 8000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1648340600.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">107.23536</span><span class="err"> </span><span class="nc">-163.15173</span><span class="err"> </span><span class="nc">-59.58964</span><span class="err"> </span><span class="nc">1050.524</span><span class="err"> </span><span class="nc">4798.979</span>
<span class="nt">Epoch</span><span class="na"> 9000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1619243400.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">109.44742</span><span class="err"> </span><span class="nc">-186.9409</span><span class="err"> </span><span class="nc">-56.53944</span><span class="err"> </span><span class="nc">1216.6432</span><span class="err"> </span><span class="nc">5454.9463</span>
<span class="nt">Epoch</span><span class="na"> 10000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1590821900.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">111.54233</span><span class="err"> </span><span class="nc">-209.91287</span><span class="err"> </span><span class="nc">-51.423084</span><span class="err"> </span><span class="nc">1385.8513</span><span class="err"> </span><span class="nc">6113.5137</span>
<span class="nt">Epoch</span><span class="na"> 11000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1563042200.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">113.54405</span><span class="err"> </span><span class="nc">-232.21953</span><span class="err"> </span><span class="nc">-44.73371</span><span class="err"> </span><span class="nc">1557.1084</span><span class="err"> </span><span class="nc">6771.7046</span>
<span class="nt">Epoch</span><span class="na"> 12000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1535855600.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">115.471565</span><span class="err"> </span><span class="nc">-253.9838</span><span class="err"> </span><span class="nc">-36.851135</span><span class="err"> </span><span class="nc">1729.535</span><span class="err"> </span><span class="nc">7429.069</span>
<span class="nt">Epoch</span><span class="na"> 13000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1509255300.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">117.33939</span><span class="err"> </span><span class="nc">-275.29697</span><span class="err"> </span><span class="nc">-28.0714</span><span class="err"> </span><span class="nc">1902.5308</span><span class="err"> </span><span class="nc">8083.9634</span>
<span class="nt">Epoch</span><span class="na"> 14000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1483227000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">119.1605</span><span class="err"> </span><span class="nc">-296.2472</span><span class="err"> </span><span class="nc">-18.618649</span><span class="err"> </span><span class="nc">2075.6094</span><span class="err"> </span><span class="nc">8735.381</span>
<span class="nt">Epoch</span><span class="na"> 15000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1457726700.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">120.94584</span><span class="err"> </span><span class="nc">-316.915</span><span class="err"> </span><span class="nc">-8.650095</span><span class="err"> </span><span class="nc">2248.3247</span><span class="err"> </span><span class="nc">9384.197</span>
<span class="nt">Epoch</span><span class="na"> 16000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1432777300.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">122.69806</span><span class="err"> </span><span class="nc">-337.30704</span><span class="err"> </span><span class="nc">1.7027153</span><span class="err"> </span><span class="nc">2420.5771</span><span class="err"> </span><span class="nc">10028.871</span>
<span class="nt">Epoch</span><span class="na"> 17000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1408365000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">124.42179</span><span class="err"> </span><span class="nc">-357.45245</span><span class="err"> </span><span class="nc">12.33499</span><span class="err"> </span><span class="nc">2592.2983</span><span class="err"> </span><span class="nc">10669.157</span>
<span class="nt">Epoch</span><span class="na"> 18000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1384480000.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">126.12332</span><span class="err"> </span><span class="nc">-377.39734</span><span class="err"> </span><span class="nc">23.168756</span><span class="err"> </span><span class="nc">2763.0933</span><span class="err"> </span><span class="nc">11305.027</span>
<span class="nt">Epoch</span><span class="na"> 19000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1361116800.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">127.80568</span><span class="err"> </span><span class="nc">-397.16415</span><span class="err"> </span><span class="nc">34.160156</span><span class="err"> </span><span class="nc">2933.0452</span><span class="err"> </span><span class="nc">11935.669</span>
<span class="nt">Epoch</span><span class="na"> 20000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1338288100.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">129.4674</span><span class="err"> </span><span class="nc">-416.72803</span><span class="err"> </span><span class="nc">45.259155</span><span class="err"> </span><span class="nc">3101.7727</span><span class="err"> </span><span class="nc">12561.179</span>
<span class="nt">Epoch</span><span class="na"> 21000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1315959700.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">131.11403</span><span class="err"> </span><span class="nc">-436.14285</span><span class="err"> </span><span class="nc">56.4436</span><span class="err"> </span><span class="nc">3269.3142</span><span class="err"> </span><span class="nc">13182.058</span>
<span class="nt">Epoch</span><span class="na"> 22000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1294164700.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">132.74377</span><span class="err"> </span><span class="nc">-455.3779</span><span class="err"> </span><span class="nc">67.6757</span><span class="err"> </span><span class="nc">3435.3833</span><span class="err"> </span><span class="nc">13796.807</span>
<span class="nt">Epoch</span><span class="na"> 23000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1272863600.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">134.35779</span><span class="err"> </span><span class="nc">-474.45316</span><span class="err"> </span><span class="nc">78.96117</span><span class="err"> </span><span class="nc">3600.264</span><span class="err"> </span><span class="nc">14406.58</span>
<span class="nt">Epoch</span><span class="na"> 24000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1252052600.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">135.9583</span><span class="err"> </span><span class="nc">-493.38254</span><span class="err"> </span><span class="nc">90.268616</span><span class="err"> </span><span class="nc">3764.0078</span><span class="err"> </span><span class="nc">15010.481</span>
<span class="nt">Epoch</span><span class="na"> 25000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1231713700.0</span><span class="err">  </span><span class="nc">a,b,c,d</span><span class="p">:</span><span class="err"> </span><span class="nc">137.54753</span><span class="err"> </span><span class="nc">-512.1876</span><span class="err"> </span><span class="nc">101.59372</span><span class="err"> </span><span class="nc">3926.4897</span><span class="err"> </span><span class="nc">15609.368</span>
<span class="nt">1231713700.0</span><span class="na"> 137.54753 -512.1876 101.59372 3926.4897 15609.368</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">predictions</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">abscissa</span><span class="p">:</span>
  <span class="n">predictions</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">coefficient1</span><span class="o">*</span><span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span> <span class="o">+</span> <span class="n">coefficient2</span><span class="o">*</span><span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span> <span class="o">+</span> <span class="n">coefficient3</span><span class="o">*</span><span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">coefficient4</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">constant</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">abscissa</span> <span class="p">,</span> <span class="n">ordinate</span><span class="p">,</span> <span class="s1">&#39;ro&#39;</span><span class="p">,</span> <span class="n">label</span> <span class="o">=</span><span class="s1">&#39;Original data&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">predictions</span><span class="p">,</span> <span class="n">label</span> <span class="o">=</span><span class="s1">&#39;Fitted line&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Quartic Regression Result&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</div>

</code></pre><img src="https://navanchauhan.github.io//assets/gciTales/03-regression/5.png"/><h3>Quintic</h3><pre><code><div class="highlight"><span></span><span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">Session</span><span class="p">()</span> <span class="k">as</span> <span class="n">sess</span><span class="p">:</span>
    <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">init</span><span class="p">)</span>
    <span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">no_of_epochs</span><span class="p">):</span>
      <span class="k">for</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">ordinate</span><span class="p">):</span>
        <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">optimizer5</span><span class="p">,</span> <span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">x</span><span class="p">,</span> <span class="n">Y</span><span class="p">:</span><span class="n">y</span><span class="p">})</span>
      <span class="k">if</span> <span class="p">(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">%</span><span class="mi">1000</span><span class="o">==</span><span class="mi">0</span><span class="p">:</span>
        <span class="n">cost</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">mse5</span><span class="p">,</span><span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">abscissa</span><span class="p">,</span><span class="n">Y</span><span class="p">:</span><span class="n">ordinate</span><span class="p">})</span>
        <span class="k">print</span><span class="p">(</span><span class="s2">&quot;Epoch&quot;</span><span class="p">,(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span> <span class="s2">&quot;: Training Cost:&quot;</span><span class="p">,</span> <span class="n">cost</span><span class="p">,</span><span class="s2">&quot; a,b,c,d,e,f:&quot;</span><span class="p">,</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">a</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">b</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">c</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">d</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">e</span><span class="p">),</span><span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">f</span><span class="p">))</span>

        <span class="n">training_cost</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">mse5</span><span class="p">,</span><span class="n">feed_dict</span><span class="o">=</span><span class="p">{</span><span class="n">X</span><span class="p">:</span><span class="n">abscissa</span><span class="p">,</span><span class="n">Y</span><span class="p">:</span><span class="n">ordinate</span><span class="p">})</span>
        <span class="n">coefficient1</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
        <span class="n">coefficient2</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
        <span class="n">coefficient3</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
        <span class="n">coefficient4</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
        <span class="n">coefficient5</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
        <span class="n">constant</span> <span class="o">=</span> <span class="n">sess</span><span class="o">.</span><span class="n">run</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="nt">Epoch</span><span class="na"> 1000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1409200100.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">7.949472</span><span class="err"> </span><span class="nc">7.46219</span><span class="err"> </span><span class="nc">55.626034</span><span class="err"> </span><span class="nc">184.29028</span><span class="err"> </span><span class="nc">484.00223</span><span class="err"> </span><span class="nc">1024.0083</span>
<span class="nt">Epoch</span><span class="na"> 2000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1306882400.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">8.732181</span><span class="err"> </span><span class="nc">-4.0085897</span><span class="err"> </span><span class="nc">73.25298</span><span class="err"> </span><span class="nc">315.90103</span><span class="err"> </span><span class="nc">904.08887</span><span class="err"> </span><span class="nc">2004.9749</span>
<span class="nt">Epoch</span><span class="na"> 3000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1212606000.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">9.732249</span><span class="err"> </span><span class="nc">-16.90125</span><span class="err"> </span><span class="nc">86.28379</span><span class="err"> </span><span class="nc">437.06552</span><span class="err"> </span><span class="nc">1305.055</span><span class="err"> </span><span class="nc">2966.2188</span>
<span class="nt">Epoch</span><span class="na"> 4000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1123640400.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">10.74851</span><span class="err"> </span><span class="nc">-29.82692</span><span class="err"> </span><span class="nc">98.59997</span><span class="err"> </span><span class="nc">555.331</span><span class="err"> </span><span class="nc">1698.4631</span><span class="err"> </span><span class="nc">3917.9155</span>
<span class="nt">Epoch</span><span class="na"> 5000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">1039694300.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">11.75426</span><span class="err"> </span><span class="nc">-42.598194</span><span class="err"> </span><span class="nc">110.698326</span><span class="err"> </span><span class="nc">671.64355</span><span class="err"> </span><span class="nc">2085.5513</span><span class="err"> </span><span class="nc">4860.8535</span>
<span class="nt">Epoch</span><span class="na"> 6000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">960663550.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">12.745439</span><span class="err"> </span><span class="nc">-55.18337</span><span class="err"> </span><span class="nc">122.644936</span><span class="err"> </span><span class="nc">786.00214</span><span class="err"> </span><span class="nc">2466.1638</span><span class="err"> </span><span class="nc">5794.3735</span>
<span class="nt">Epoch</span><span class="na"> 7000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">886438340.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">13.721028</span><span class="err"> </span><span class="nc">-67.57168</span><span class="err"> </span><span class="nc">134.43822</span><span class="err"> </span><span class="nc">898.3691</span><span class="err"> </span><span class="nc">2839.9958</span><span class="err"> </span><span class="nc">6717.659</span>
<span class="nt">Epoch</span><span class="na"> 8000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">816913100.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">14.679965</span><span class="err"> </span><span class="nc">-79.75113</span><span class="err"> </span><span class="nc">146.07385</span><span class="err"> </span><span class="nc">1008.66895</span><span class="err"> </span><span class="nc">3206.6692</span><span class="err"> </span><span class="nc">7629.812</span>
<span class="nt">Epoch</span><span class="na"> 9000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">751971500.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">15.62181</span><span class="err"> </span><span class="nc">-91.71608</span><span class="err"> </span><span class="nc">157.55713</span><span class="err"> </span><span class="nc">1116.7715</span><span class="err"> </span><span class="nc">3565.8323</span><span class="err"> </span><span class="nc">8529.976</span>
<span class="nt">Epoch</span><span class="na"> 10000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">691508740.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">16.545347</span><span class="err"> </span><span class="nc">-103.4531</span><span class="err"> </span><span class="nc">168.88321</span><span class="err"> </span><span class="nc">1222.6348</span><span class="err"> </span><span class="nc">3916.9785</span><span class="err"> </span><span class="nc">9416.236</span>
<span class="nt">Epoch</span><span class="na"> 11000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">635382000.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">17.450052</span><span class="err"> </span><span class="nc">-114.954254</span><span class="err"> </span><span class="nc">180.03932</span><span class="err"> </span><span class="nc">1326.1565</span><span class="err"> </span><span class="nc">4259.842</span><span class="err"> </span><span class="nc">10287.99</span>
<span class="nt">Epoch</span><span class="na"> 12000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">583477250.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">18.334944</span><span class="err"> </span><span class="nc">-126.20821</span><span class="err"> </span><span class="nc">191.02948</span><span class="err"> </span><span class="nc">1427.2095</span><span class="err"> </span><span class="nc">4593.8</span><span class="err"> </span><span class="nc">11143.449</span>
<span class="nt">Epoch</span><span class="na"> 13000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">535640400.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">19.198917</span><span class="err"> </span><span class="nc">-137.20206</span><span class="err"> </span><span class="nc">201.84718</span><span class="err"> </span><span class="nc">1525.6926</span><span class="err"> </span><span class="nc">4918.5327</span><span class="err"> </span><span class="nc">11981.633</span>
<span class="nt">Epoch</span><span class="na"> 14000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">491722240.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">20.041153</span><span class="err"> </span><span class="nc">-147.92719</span><span class="err"> </span><span class="nc">212.49709</span><span class="err"> </span><span class="nc">1621.5496</span><span class="err"> </span><span class="nc">5233.627</span><span class="err"> </span><span class="nc">12800.468</span>
<span class="nt">Epoch</span><span class="na"> 15000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">451559520.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">20.860966</span><span class="err"> </span><span class="nc">-158.37456</span><span class="err"> </span><span class="nc">222.97133</span><span class="err"> </span><span class="nc">1714.7141</span><span class="err"> </span><span class="nc">5538.676</span><span class="err"> </span><span class="nc">13598.337</span>
<span class="nt">Epoch</span><span class="na"> 16000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">414988960.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">21.657421</span><span class="err"> </span><span class="nc">-168.53406</span><span class="err"> </span><span class="nc">233.27422</span><span class="err"> </span><span class="nc">1805.0874</span><span class="err"> </span><span class="nc">5833.1978</span><span class="err"> </span><span class="nc">14373.658</span>
<span class="nt">Epoch</span><span class="na"> 17000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">381837920.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">22.429693</span><span class="err"> </span><span class="nc">-178.39536</span><span class="err"> </span><span class="nc">243.39914</span><span class="err"> </span><span class="nc">1892.5883</span><span class="err"> </span><span class="nc">6116.847</span><span class="err"> </span><span class="nc">15124.394</span>
<span class="nt">Epoch</span><span class="na"> 18000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">351931300.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">23.176882</span><span class="err"> </span><span class="nc">-187.94789</span><span class="err"> </span><span class="nc">253.3445</span><span class="err"> </span><span class="nc">1977.137</span><span class="err"> </span><span class="nc">6389.117</span><span class="err"> </span><span class="nc">15848.417</span>
<span class="nt">Epoch</span><span class="na"> 19000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">325074400.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">23.898485</span><span class="err"> </span><span class="nc">-197.18741</span><span class="err"> </span><span class="nc">263.12512</span><span class="err"> </span><span class="nc">2058.6716</span><span class="err"> </span><span class="nc">6649.8037</span><span class="err"> </span><span class="nc">16543.95</span>
<span class="nt">Epoch</span><span class="na"> 20000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">301073570.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">24.593851</span><span class="err"> </span><span class="nc">-206.10497</span><span class="err"> </span><span class="nc">272.72385</span><span class="err"> </span><span class="nc">2137.1797</span><span class="err"> </span><span class="nc">6898.544</span><span class="err"> </span><span class="nc">17209.367</span>
<span class="nt">Epoch</span><span class="na"> 21000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">279727000.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">25.262104</span><span class="err"> </span><span class="nc">-214.69217</span><span class="err"> </span><span class="nc">282.14642</span><span class="err"> </span><span class="nc">2212.6372</span><span class="err"> </span><span class="nc">7135.217</span><span class="err"> </span><span class="nc">17842.854</span>
<span class="nt">Epoch</span><span class="na"> 22000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">260845550.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">25.903376</span><span class="err"> </span><span class="nc">-222.94969</span><span class="err"> </span><span class="nc">291.4003</span><span class="err"> </span><span class="nc">2284.9844</span><span class="err"> </span><span class="nc">7359.4644</span><span class="err"> </span><span class="nc">18442.408</span>
<span class="nt">Epoch</span><span class="na"> 23000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">244218030.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">26.517094</span><span class="err"> </span><span class="nc">-230.8697</span><span class="err"> </span><span class="nc">300.45532</span><span class="err"> </span><span class="nc">2354.3003</span><span class="err"> </span><span class="nc">7571.261</span><span class="err"> </span><span class="nc">19007.49</span>
<span class="nt">Epoch</span><span class="na"> 24000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">229660080.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">27.102589</span><span class="err"> </span><span class="nc">-238.44817</span><span class="err"> </span><span class="nc">309.35342</span><span class="err"> </span><span class="nc">2420.4185</span><span class="err"> </span><span class="nc">7770.5728</span><span class="err"> </span><span class="nc">19536.19</span>
<span class="nt">Epoch</span><span class="na"> 25000 </span><span class="p">:</span><span class="err"> </span><span class="nc">Training</span><span class="err"> </span><span class="nc">Cost</span><span class="p">:</span><span class="err"> </span><span class="nc">216972400.0</span><span class="err">  </span><span class="nc">a,b,c,d,e,f</span><span class="p">:</span><span class="err"> </span><span class="nc">27.660324</span><span class="err"> </span><span class="nc">-245.69016</span><span class="err"> </span><span class="nc">318.10062</span><span class="err"> </span><span class="nc">2483.3608</span><span class="err"> </span><span class="nc">7957.354</span><span class="err"> </span><span class="nc">20027.707</span>
<span class="nt">216972400.0</span><span class="na"> 27.660324 -245.69016 318.10062 2483.3608 7957.354 20027.707</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">predictions</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">abscissa</span><span class="p">:</span>
  <span class="n">predictions</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">coefficient1</span><span class="o">*</span><span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span> <span class="o">+</span> <span class="n">coefficient2</span><span class="o">*</span><span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span> <span class="o">+</span> <span class="n">coefficient3</span><span class="o">*</span><span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span> <span class="o">+</span> <span class="n">coefficient4</span><span class="o">*</span><span class="nb">pow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">coefficient5</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">constant</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">abscissa</span> <span class="p">,</span> <span class="n">ordinate</span><span class="p">,</span> <span class="s1">&#39;ro&#39;</span><span class="p">,</span> <span class="n">label</span> <span class="o">=</span><span class="s1">&#39;Original data&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">abscissa</span><span class="p">,</span> <span class="n">predictions</span><span class="p">,</span> <span class="n">label</span> <span class="o">=</span><span class="s1">&#39;Fitted line&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Quintic Regression Result&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</div>

</code></pre><img src="https://navanchauhan.github.io//assets/gciTales/03-regression/6.png"/><h2>Results and Conclusion</h2><p>You just learnt Polynomial Regression using TensorFlow!</p><h2>Notes</h2><h3>Overfitting</h3><blockquote><p>&gt; Overfitting refers to a model that models the training data too well.Overfitting happens when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data. This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize.</p></blockquote><blockquote><p>Source: Machine Learning Mastery</p></blockquote><p>Basically if you train your machine learning model on a small dataset for a really large number of epochs, the model will learn all the deformities/noise in the data and will actually think that it is a normal part. Therefore when it will see some new data, it will discard that new data as noise and will impact the accuracy of the model in a negative manner</p>]]></content:encoded></item><item><guid isPermaLink="true">https://navanchauhan.github.io/posts/2019-12-10-TensorFlow-Model-Prediction</guid><title>Making Predictions using Image Classifier (TensorFlow)</title><description>Making predictions for image classification models built using TensorFlow</description><link>https://navanchauhan.github.io/posts/2019-12-10-TensorFlow-Model-Prediction</link><pubDate>Tue, 10 Dec 2019 11:10:00 +0530</pubDate><content:encoded><![CDATA[<h1>Making Predictions using Image Classifier (TensorFlow)</h1><p><em>This was tested on TF 2.x and works as of 2019-12-10</em></p><p>If you want to understand how to make your own custom image classifier, please refer to my previous post.</p><p>If you followed my last post, then you created a model which took an image of dimensions 50x50 as an input.</p><p>First we import the following if we have not imported these before</p><pre><code><div class="highlight"><span></span><span class="kn">import</span> <span class="nn">cv2</span>
<span class="kn">import</span> <span class="nn">os</span>
</div>

</code></pre><p>Then we read the file using OpenCV.</p><pre><code><div class="highlight"><span></span><span class="n">image</span><span class="o">=</span><span class="n">cv2</span><span class="o">.</span><span class="n">imread</span><span class="p">(</span><span class="n">imagePath</span><span class="p">)</span>
</div>

</code></pre><p>The cv2. imread() function returns a NumPy array representing the image. Therefore, we need to convert it before we can use it.</p><pre><code><div class="highlight"><span></span><span class="n">image_from_array</span> <span class="o">=</span> <span class="n">Image</span><span class="o">.</span><span class="n">fromarray</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="s1">&#39;RGB&#39;</span><span class="p">)</span>
</div>

</code></pre><p>Then we resize the image</p><pre><code><div class="highlight"><span></span><span class="n">size_image</span> <span class="o">=</span> <span class="n">image_from_array</span><span class="o">.</span><span class="n">resize</span><span class="p">((</span><span class="mi">50</span><span class="p">,</span><span class="mi">50</span><span class="p">))</span>
</div>

</code></pre><p>After this we create a batch consisting of only one image</p><pre><code><div class="highlight"><span></span><span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">expand_dims</span><span class="p">(</span><span class="n">size_image</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
</div>

</code></pre><p>We then convert this uint8 datatype to a float32 datatype</p><pre><code><div class="highlight"><span></span><span class="n">img</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">cast</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
</div>

</code></pre><p>Finally we make the prediction</p><pre><code><div class="highlight"><span></span><span class="k">print</span><span class="p">([</span><span class="s1">&#39;Infected&#39;</span><span class="p">,</span><span class="s1">&#39;Uninfected&#39;</span><span class="p">][</span><span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">img</span><span class="p">))])</span>
</div>

</code></pre><p><code>Infected</code></p>]]></content:encoded></item><item><guid isPermaLink="true">https://navanchauhan.github.io/posts/2019-12-08-Image-Classifier-Tensorflow</guid><title>Creating a Custom Image Classifier using Tensorflow 2.x and Keras for Detecting Malaria</title><description>Tutorial on creating an image classifier model using TensorFlow which detects malaria</description><link>https://navanchauhan.github.io/posts/2019-12-08-Image-Classifier-Tensorflow</link><pubDate>Sun, 8 Dec 2019 14:16:00 +0530</pubDate><content:encoded><![CDATA[<h1>Creating a Custom Image Classifier using Tensorflow 2.x and Keras for Detecting Malaria</h1><p><strong>Done during Google Code-In. Org: Tensorflow.</strong></p><h2>Imports</h2><pre><code><div class="highlight"><span></span><span class="o">%</span><span class="n">tensorflow_version</span> <span class="mf">2.</span><span class="n">x</span> <span class="c1">#This is for telling Colab that you want to use TF 2.0, ignore if running on local machine</span>

<span class="kn">from</span> <span class="nn">PIL</span> <span class="kn">import</span> <span class="n">Image</span> <span class="c1"># We use the PIL Library to resize images</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">os</span>
<span class="kn">import</span> <span class="nn">cv2</span>
<span class="kn">import</span> <span class="nn">tensorflow</span> <span class="kn">as</span> <span class="nn">tf</span>
<span class="kn">from</span> <span class="nn">tensorflow.keras</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">models</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">keras.models</span> <span class="kn">import</span> <span class="n">Sequential</span>
<span class="kn">from</span> <span class="nn">keras.layers</span> <span class="kn">import</span> <span class="n">Conv2D</span><span class="p">,</span><span class="n">MaxPooling2D</span><span class="p">,</span><span class="n">Dense</span><span class="p">,</span><span class="n">Flatten</span><span class="p">,</span><span class="n">Dropout</span>
</div>

</code></pre><h2>Dataset</h2><h3>Fetching the Data</h3><pre><code><div class="highlight"><span></span><span class="err">!</span><span class="n">wget</span> <span class="n">ftp</span><span class="p">:</span><span class="o">//</span><span class="n">lhcftp</span><span class="o">.</span><span class="n">nlm</span><span class="o">.</span><span class="n">nih</span><span class="o">.</span><span class="n">gov</span><span class="o">/</span><span class="n">Open</span><span class="o">-</span><span class="n">Access</span><span class="o">-</span><span class="n">Datasets</span><span class="o">/</span><span class="n">Malaria</span><span class="o">/</span><span class="n">cell_images</span><span class="o">.</span><span class="n">zip</span>
<span class="err">!</span><span class="n">unzip</span> <span class="n">cell_images</span><span class="o">.</span><span class="n">zip</span>
</div>

</code></pre><h3>Processing the Data</h3><p>We resize all the images as 50x50 and add the numpy array of that image as well as their label names (Infected or Not) to common arrays.</p><pre><code><div class="highlight"><span></span><span class="n">data</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">labels</span> <span class="o">=</span> <span class="p">[]</span>

<span class="n">Parasitized</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">listdir</span><span class="p">(</span><span class="s2">&quot;./cell_images/Parasitized/&quot;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">parasite</span> <span class="ow">in</span> <span class="n">Parasitized</span><span class="p">:</span>
    <span class="k">try</span><span class="p">:</span>
        <span class="n">image</span><span class="o">=</span><span class="n">cv2</span><span class="o">.</span><span class="n">imread</span><span class="p">(</span><span class="s2">&quot;./cell_images/Parasitized/&quot;</span><span class="o">+</span><span class="n">parasite</span><span class="p">)</span>
        <span class="n">image_from_array</span> <span class="o">=</span> <span class="n">Image</span><span class="o">.</span><span class="n">fromarray</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="s1">&#39;RGB&#39;</span><span class="p">)</span>
        <span class="n">size_image</span> <span class="o">=</span> <span class="n">image_from_array</span><span class="o">.</span><span class="n">resize</span><span class="p">((</span><span class="mi">50</span><span class="p">,</span> <span class="mi">50</span><span class="p">))</span>
        <span class="n">data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">size_image</span><span class="p">))</span>
        <span class="n">labels</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
    <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
        <span class="k">print</span><span class="p">(</span><span class="s2">&quot;&quot;</span><span class="p">)</span>

<span class="n">Uninfected</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">listdir</span><span class="p">(</span><span class="s2">&quot;./cell_images/Uninfected/&quot;</span><span class="p">)</span>
<span class="k">for</span> <span class="n">uninfect</span> <span class="ow">in</span> <span class="n">Uninfected</span><span class="p">:</span>
    <span class="k">try</span><span class="p">:</span>
        <span class="n">image</span><span class="o">=</span><span class="n">cv2</span><span class="o">.</span><span class="n">imread</span><span class="p">(</span><span class="s2">&quot;./cell_images/Uninfected/&quot;</span><span class="o">+</span><span class="n">uninfect</span><span class="p">)</span>
        <span class="n">image_from_array</span> <span class="o">=</span> <span class="n">Image</span><span class="o">.</span><span class="n">fromarray</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="s1">&#39;RGB&#39;</span><span class="p">)</span>
        <span class="n">size_image</span> <span class="o">=</span> <span class="n">image_from_array</span><span class="o">.</span><span class="n">resize</span><span class="p">((</span><span class="mi">50</span><span class="p">,</span> <span class="mi">50</span><span class="p">))</span>
        <span class="n">data</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">size_image</span><span class="p">))</span>
        <span class="n">labels</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
    <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
        <span class="k">print</span><span class="p">(</span><span class="s2">&quot;&quot;</span><span class="p">)</span>
</div>

</code></pre><h3>Splitting Data</h3><pre><code><div class="highlight"><span></span><span class="n">df</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">labels</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">labels</span><span class="p">)</span>
<span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">)</span> <span class="o">=</span> <span class="n">df</span><span class="p">[(</span><span class="nb">int</span><span class="p">)(</span><span class="mf">0.1</span><span class="o">*</span><span class="nb">len</span><span class="p">(</span><span class="n">df</span><span class="p">)):],</span><span class="n">df</span><span class="p">[:(</span><span class="nb">int</span><span class="p">)(</span><span class="mf">0.1</span><span class="o">*</span><span class="nb">len</span><span class="p">(</span><span class="n">df</span><span class="p">))]</span>
<span class="p">(</span><span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span><span class="p">)</span> <span class="o">=</span> <span class="n">labels</span><span class="p">[(</span><span class="nb">int</span><span class="p">)(</span><span class="mf">0.1</span><span class="o">*</span><span class="nb">len</span><span class="p">(</span><span class="n">labels</span><span class="p">)):],</span><span class="n">labels</span><span class="p">[:(</span><span class="nb">int</span><span class="p">)(</span><span class="mf">0.1</span><span class="o">*</span><span class="nb">len</span><span class="p">(</span><span class="n">labels</span><span class="p">))]</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">s</span><span class="p">=</span><span class="n">np</span><span class="p">.</span><span class="n">arange</span><span class="p">(</span><span class="n">X_train</span><span class="p">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="n">np</span><span class="p">.</span><span class="n">random</span><span class="p">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="n">X_train</span><span class="p">=</span><span class="n">X_train</span><span class="p">[</span><span class="n">s</span><span class="p">]</span>
<span class="n">y_train</span><span class="p">=</span><span class="n">y_train</span><span class="p">[</span><span class="n">s</span><span class="p">]</span>
<span class="n">X_train</span> <span class="p">=</span> <span class="n">X_train</span><span class="o">/</span><span class="mf">255.0</span>
</div>

</code></pre><h2>Model</h2><h3>Creating Model</h3><p>By creating a sequential model, we create a linear stack of layers.</p><p><em>Note: The input shape for the first layer is 50,50 which corresponds with the sizes of the resized images</em></p><pre><code><div class="highlight"><span></span><span class="n">model</span> <span class="o">=</span> <span class="n">models</span><span class="o">.</span><span class="n">Sequential</span><span class="p">()</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">Conv2D</span><span class="p">(</span><span class="n">filters</span><span class="o">=</span><span class="mi">16</span><span class="p">,</span> <span class="n">kernel_size</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">,</span> <span class="n">activation</span><span class="o">=</span><span class="s1">&#39;relu&#39;</span><span class="p">,</span> <span class="n">input_shape</span><span class="o">=</span><span class="p">(</span><span class="mi">50</span><span class="p">,</span><span class="mi">50</span><span class="p">,</span><span class="mi">3</span><span class="p">)))</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">MaxPooling2D</span><span class="p">(</span><span class="n">pool_size</span><span class="o">=</span><span class="mi">2</span><span class="p">))</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">Conv2D</span><span class="p">(</span><span class="n">filters</span><span class="o">=</span><span class="mi">32</span><span class="p">,</span><span class="n">kernel_size</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span><span class="n">padding</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">,</span><span class="n">activation</span><span class="o">=</span><span class="s1">&#39;relu&#39;</span><span class="p">))</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">MaxPooling2D</span><span class="p">(</span><span class="n">pool_size</span><span class="o">=</span><span class="mi">2</span><span class="p">))</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">Conv2D</span><span class="p">(</span><span class="n">filters</span><span class="o">=</span><span class="mi">64</span><span class="p">,</span><span class="n">kernel_size</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span><span class="n">padding</span><span class="o">=</span><span class="s2">&quot;same&quot;</span><span class="p">,</span><span class="n">activation</span><span class="o">=</span><span class="s2">&quot;relu&quot;</span><span class="p">))</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">MaxPooling2D</span><span class="p">(</span><span class="n">pool_size</span><span class="o">=</span><span class="mi">2</span><span class="p">))</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">Dropout</span><span class="p">(</span><span class="mf">0.2</span><span class="p">))</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">Flatten</span><span class="p">())</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">500</span><span class="p">,</span><span class="n">activation</span><span class="o">=</span><span class="s2">&quot;relu&quot;</span><span class="p">))</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">Dropout</span><span class="p">(</span><span class="mf">0.2</span><span class="p">))</span>
<span class="n">model</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">layers</span><span class="o">.</span><span class="n">Dense</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="n">activation</span><span class="o">=</span><span class="s2">&quot;softmax&quot;</span><span class="p">))</span><span class="c1">#2 represent output layer neurons </span>
<span class="n">model</span><span class="o">.</span><span class="n">summary</span><span class="p">()</span>
</div>

</code></pre><h3>Compiling Model</h3><p>We use the adam optimiser as it is an adaptive learning rate optimization algorithm that's been designed specifically for <em>training</em> deep neural networks, which means it changes its learning rate automaticaly to get the best results</p><pre><code><div class="highlight"><span></span><span class="n">model</span><span class="o">.</span><span class="n">compile</span><span class="p">(</span><span class="n">optimizer</span><span class="o">=</span><span class="s2">&quot;adam&quot;</span><span class="p">,</span>
              <span class="n">loss</span><span class="o">=</span><span class="s2">&quot;sparse_categorical_crossentropy&quot;</span><span class="p">,</span> 
             <span class="n">metrics</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;accuracy&quot;</span><span class="p">])</span>
</div>

</code></pre><h3>Training Model</h3><p>We train the model for 10 epochs on the training data and then validate it using the testing data</p><pre><code><div class="highlight"><span></span><span class="n">history</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span><span class="n">y_train</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">validation_data</span><span class="o">=</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span><span class="n">y_test</span><span class="p">))</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">Train</span> <span class="n">on</span> <span class="mi">24803</span> <span class="n">samples</span><span class="p">,</span> <span class="n">validate</span> <span class="n">on</span> <span class="mi">2755</span> <span class="n">samples</span>
<span class="n">Epoch</span> <span class="mi">1</span><span class="o">/</span><span class="mi">10</span>
<span class="mi">24803</span><span class="o">/</span><span class="mi">24803</span> <span class="p">[</span><span class="o">==============================</span><span class="p">]</span> <span class="o">-</span> <span class="mi">57</span><span class="n">s</span> <span class="mi">2</span><span class="n">ms</span><span class="o">/</span><span class="n">sample</span> <span class="o">-</span> <span class="n">loss</span><span class="p">:</span> <span class="mf">0.0786</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">:</span> <span class="mf">0.9729</span> <span class="o">-</span> <span class="n">val_loss</span><span class="p">:</span> <span class="mf">0.0000e+00</span> <span class="o">-</span> <span class="n">val_accuracy</span><span class="p">:</span> <span class="mf">1.0000</span>
<span class="n">Epoch</span> <span class="mi">2</span><span class="o">/</span><span class="mi">10</span>
<span class="mi">24803</span><span class="o">/</span><span class="mi">24803</span> <span class="p">[</span><span class="o">==============================</span><span class="p">]</span> <span class="o">-</span> <span class="mi">58</span><span class="n">s</span> <span class="mi">2</span><span class="n">ms</span><span class="o">/</span><span class="n">sample</span> <span class="o">-</span> <span class="n">loss</span><span class="p">:</span> <span class="mf">0.0746</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">:</span> <span class="mf">0.9731</span> <span class="o">-</span> <span class="n">val_loss</span><span class="p">:</span> <span class="mf">0.0290</span> <span class="o">-</span> <span class="n">val_accuracy</span><span class="p">:</span> <span class="mf">0.9996</span>
<span class="n">Epoch</span> <span class="mi">3</span><span class="o">/</span><span class="mi">10</span>
<span class="mi">24803</span><span class="o">/</span><span class="mi">24803</span> <span class="p">[</span><span class="o">==============================</span><span class="p">]</span> <span class="o">-</span> <span class="mi">58</span><span class="n">s</span> <span class="mi">2</span><span class="n">ms</span><span class="o">/</span><span class="n">sample</span> <span class="o">-</span> <span class="n">loss</span><span class="p">:</span> <span class="mf">0.0672</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">:</span> <span class="mf">0.9764</span> <span class="o">-</span> <span class="n">val_loss</span><span class="p">:</span> <span class="mf">0.0000e+00</span> <span class="o">-</span> <span class="n">val_accuracy</span><span class="p">:</span> <span class="mf">1.0000</span>
<span class="n">Epoch</span> <span class="mi">4</span><span class="o">/</span><span class="mi">10</span>
<span class="mi">24803</span><span class="o">/</span><span class="mi">24803</span> <span class="p">[</span><span class="o">==============================</span><span class="p">]</span> <span class="o">-</span> <span class="mi">58</span><span class="n">s</span> <span class="mi">2</span><span class="n">ms</span><span class="o">/</span><span class="n">sample</span> <span class="o">-</span> <span class="n">loss</span><span class="p">:</span> <span class="mf">0.0601</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">:</span> <span class="mf">0.9789</span> <span class="o">-</span> <span class="n">val_loss</span><span class="p">:</span> <span class="mf">0.0000e+00</span> <span class="o">-</span> <span class="n">val_accuracy</span><span class="p">:</span> <span class="mf">1.0000</span>
<span class="n">Epoch</span> <span class="mi">5</span><span class="o">/</span><span class="mi">10</span>
<span class="mi">24803</span><span class="o">/</span><span class="mi">24803</span> <span class="p">[</span><span class="o">==============================</span><span class="p">]</span> <span class="o">-</span> <span class="mi">58</span><span class="n">s</span> <span class="mi">2</span><span class="n">ms</span><span class="o">/</span><span class="n">sample</span> <span class="o">-</span> <span class="n">loss</span><span class="p">:</span> <span class="mf">0.0558</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">:</span> <span class="mf">0.9804</span> <span class="o">-</span> <span class="n">val_loss</span><span class="p">:</span> <span class="mf">0.0000e+00</span> <span class="o">-</span> <span class="n">val_accuracy</span><span class="p">:</span> <span class="mf">1.0000</span>
<span class="n">Epoch</span> <span class="mi">6</span><span class="o">/</span><span class="mi">10</span>
<span class="mi">24803</span><span class="o">/</span><span class="mi">24803</span> <span class="p">[</span><span class="o">==============================</span><span class="p">]</span> <span class="o">-</span> <span class="mi">57</span><span class="n">s</span> <span class="mi">2</span><span class="n">ms</span><span class="o">/</span><span class="n">sample</span> <span class="o">-</span> <span class="n">loss</span><span class="p">:</span> <span class="mf">0.0513</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">:</span> <span class="mf">0.9819</span> <span class="o">-</span> <span class="n">val_loss</span><span class="p">:</span> <span class="mf">0.0000e+00</span> <span class="o">-</span> <span class="n">val_accuracy</span><span class="p">:</span> <span class="mf">1.0000</span>
<span class="n">Epoch</span> <span class="mi">7</span><span class="o">/</span><span class="mi">10</span>
<span class="mi">24803</span><span class="o">/</span><span class="mi">24803</span> <span class="p">[</span><span class="o">==============================</span><span class="p">]</span> <span class="o">-</span> <span class="mi">58</span><span class="n">s</span> <span class="mi">2</span><span class="n">ms</span><span class="o">/</span><span class="n">sample</span> <span class="o">-</span> <span class="n">loss</span><span class="p">:</span> <span class="mf">0.0452</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">:</span> <span class="mf">0.9849</span> <span class="o">-</span> <span class="n">val_loss</span><span class="p">:</span> <span class="mf">0.3190</span> <span class="o">-</span> <span class="n">val_accuracy</span><span class="p">:</span> <span class="mf">0.9985</span>
<span class="n">Epoch</span> <span class="mi">8</span><span class="o">/</span><span class="mi">10</span>
<span class="mi">24803</span><span class="o">/</span><span class="mi">24803</span> <span class="p">[</span><span class="o">==============================</span><span class="p">]</span> <span class="o">-</span> <span class="mi">58</span><span class="n">s</span> <span class="mi">2</span><span class="n">ms</span><span class="o">/</span><span class="n">sample</span> <span class="o">-</span> <span class="n">loss</span><span class="p">:</span> <span class="mf">0.0404</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">:</span> <span class="mf">0.9858</span> <span class="o">-</span> <span class="n">val_loss</span><span class="p">:</span> <span class="mf">0.0000e+00</span> <span class="o">-</span> <span class="n">val_accuracy</span><span class="p">:</span> <span class="mf">1.0000</span>
<span class="n">Epoch</span> <span class="mi">9</span><span class="o">/</span><span class="mi">10</span>
<span class="mi">24803</span><span class="o">/</span><span class="mi">24803</span> <span class="p">[</span><span class="o">==============================</span><span class="p">]</span> <span class="o">-</span> <span class="mi">58</span><span class="n">s</span> <span class="mi">2</span><span class="n">ms</span><span class="o">/</span><span class="n">sample</span> <span class="o">-</span> <span class="n">loss</span><span class="p">:</span> <span class="mf">0.0352</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">:</span> <span class="mf">0.9878</span> <span class="o">-</span> <span class="n">val_loss</span><span class="p">:</span> <span class="mf">0.0000e+00</span> <span class="o">-</span> <span class="n">val_accuracy</span><span class="p">:</span> <span class="mf">1.0000</span>
<span class="n">Epoch</span> <span class="mi">10</span><span class="o">/</span><span class="mi">10</span>
<span class="mi">24803</span><span class="o">/</span><span class="mi">24803</span> <span class="p">[</span><span class="o">==============================</span><span class="p">]</span> <span class="o">-</span> <span class="mi">58</span><span class="n">s</span> <span class="mi">2</span><span class="n">ms</span><span class="o">/</span><span class="n">sample</span> <span class="o">-</span> <span class="n">loss</span><span class="p">:</span> <span class="mf">0.0373</span> <span class="o">-</span> <span class="n">accuracy</span><span class="p">:</span> <span class="mf">0.9865</span> <span class="o">-</span> <span class="n">val_loss</span><span class="p">:</span> <span class="mf">0.0000e+00</span> <span class="o">-</span> <span class="n">val_accuracy</span><span class="p">:</span> <span class="mf">1.0000</span>
</div>

</code></pre><h3>Results</h3><pre><code><div class="highlight"><span></span><span class="n">accuracy</span> <span class="o">=</span> <span class="n">history</span><span class="o">.</span><span class="n">history</span><span class="p">[</span><span class="s1">&#39;accuracy&#39;</span><span class="p">][</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="mi">100</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">history</span><span class="o">.</span><span class="n">history</span><span class="p">[</span><span class="s1">&#39;loss&#39;</span><span class="p">][</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="mi">100</span>
<span class="n">val_accuracy</span> <span class="o">=</span> <span class="n">history</span><span class="o">.</span><span class="n">history</span><span class="p">[</span><span class="s1">&#39;val_accuracy&#39;</span><span class="p">][</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="mi">100</span>
<span class="n">val_loss</span> <span class="o">=</span> <span class="n">history</span><span class="o">.</span><span class="n">history</span><span class="p">[</span><span class="s1">&#39;val_loss&#39;</span><span class="p">][</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">*</span><span class="mi">100</span>

<span class="k">print</span><span class="p">(</span>
    <span class="s1">&#39;Accuracy:&#39;</span><span class="p">,</span> <span class="n">accuracy</span><span class="p">,</span>
    <span class="s1">&#39;</span><span class="se">\n</span><span class="s1">Loss:&#39;</span><span class="p">,</span> <span class="n">loss</span><span class="p">,</span>
    <span class="s1">&#39;</span><span class="se">\n</span><span class="s1">Validation Accuracy:&#39;</span><span class="p">,</span> <span class="n">val_accuracy</span><span class="p">,</span>
    <span class="s1">&#39;</span><span class="se">\n</span><span class="s1">Validation Loss:&#39;</span><span class="p">,</span> <span class="n">val_loss</span>
<span class="p">)</span>
</div>

</code></pre><pre><code><div class="highlight"><span></span><span class="n">Accuracy</span><span class="p">:</span> <span class="mf">98.64532351493835</span> 
<span class="n">Loss</span><span class="p">:</span> <span class="mf">3.732407123270176</span> 
<span class="n">Validation</span> <span class="n">Accuracy</span><span class="p">:</span> <span class="mf">100.0</span> 
<span class="n">Validation</span> <span class="n">Loss</span><span class="p">:</span> <span class="mf">0.0</span>
</div>

</code></pre><p>We have achieved 98% Accuracy!</p><p><a href="https://colab.research.google.com/drive/1ZswDsxLwYZEnev89MzlL5Lwt6ut7iwp- "Colab Notebook"">Link to Colab Notebook</a></p>]]></content:encoded></item><item><guid isPermaLink="true">https://navanchauhan.github.io/posts/2019-12-08-Splitting-Zips</guid><title>Splitting ZIPs into Multiple Parts</title><description>Short code snippet for splitting zips.</description><link>https://navanchauhan.github.io/posts/2019-12-08-Splitting-Zips</link><pubDate>Sun, 8 Dec 2019 13:27:00 +0530</pubDate><content:encoded><![CDATA[<h1>Splitting ZIPs into Multiple Parts</h1><p><strong>Tested on macOS</strong></p><p>Creating the archive:</p><pre><code><div class="highlight"><span></span><span class="nt">zip</span><span class="na"> -r -s 5 oodlesofnoodles.zip website/</span>
</div>

</code></pre><p>5 stands for each split files' size (in mb, kb and gb can also be specified)</p><p>For encrypting the zip:</p><pre><code><div class="highlight"><span></span><span class="nt">zip</span><span class="na"> -er -s 5 oodlesofnoodles.zip website</span>
</div>

</code></pre><p>Extracting Files</p><p>First we need to collect all parts, then</p><pre><code><div class="highlight"><span></span><span class="nt">zip</span><span class="na"> -F oodlesofnoodles.zip --out merged.zip</span>
</div>

</code></pre>]]></content:encoded></item><item><guid isPermaLink="true">https://navanchauhan.github.io/publications/2019-05-14-Detecting-Driver-Fatigue-Over-Speeding-and-Speeding-up-Post-Accident-Response</guid><title>Detecting Driver Fatigue, Over-Speeding, and Speeding up Post-Accident Response</title><description>This paper is about Detecting Driver Fatigue, Over-Speeding, and Speeding up Post-Accident Response.</description><link>https://navanchauhan.github.io/publications/2019-05-14-Detecting-Driver-Fatigue-Over-Speeding-and-Speeding-up-Post-Accident-Response</link><pubDate>Tue, 14 May 2019 02:42:00 +0530</pubDate><content:encoded><![CDATA[<h1>Detecting Driver Fatigue, Over-Speeding, and Speeding up Post-Accident Response</h1><blockquote><p>Based on the project showcased at Toyota Hackathon, IITD - 17/18th December 2018</p></blockquote><p><a href="https://www.irjet.net/archives/V6/i5/IRJET-V6I5318.pdf">Download paper here</a></p><p>Recommended citation:</p><h3>ATP</h3><pre><code><div class="highlight"><span></span><span class="n">Chauhan</span><span class="p">,</span> <span class="n">N</span><span class="p">.</span> <span class="p">(</span><span class="mi">2019</span><span class="p">).</span> <span class="p">&amp;</span><span class="n">quot</span><span class="p">;</span><span class="n">Detecting</span> <span class="n">Driver</span> <span class="n">Fatigue</span><span class="p">,</span> <span class="n">Over</span><span class="o">-</span><span class="n">Speeding</span><span class="p">,</span> <span class="n">and</span> <span class="n">Speeding</span> <span class="n">up</span> <span class="n">Post</span><span class="o">-</span><span class="n">Accident</span> <span class="n">Response</span><span class="p">.&amp;</span><span class="n">quot</span><span class="p">;</span> <span class="p">&lt;</span><span class="n">i</span><span class="p">&gt;</span><span class="n">International</span> <span class="n">Research</span> <span class="n">Journal</span> <span class="n">of</span> <span class="n">Engineering</span> <span class="n">and</span> <span class="n">Technology</span> <span class="p">(</span><span class="n">IRJET</span><span class="p">),</span> <span class="mi">6</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span><span class="o">&lt;/</span><span class="n">i</span><span class="p">&gt;.</span>
</div>

</code></pre><h3>BibTeX</h3><pre><code><div class="highlight"><span></span><span class="p">@</span><span class="n">article</span><span class="p">{</span><span class="n">chauhan_2019</span><span class="p">,</span> <span class="n">title</span><span class="p">={</span><span class="n">Detecting</span> <span class="n">Driver</span> <span class="n">Fatigue</span><span class="p">,</span> <span class="n">Over</span><span class="o">-</span><span class="n">Speeding</span><span class="p">,</span> <span class="n">and</span> <span class="n">Speeding</span> <span class="n">up</span> <span class="n">Post</span><span class="o">-</span><span class="n">Accident</span> <span class="n">Response</span><span class="p">},</span> <span class="n">volume</span><span class="p">={</span><span class="mi">6</span><span class="p">},</span> <span class="n">url</span><span class="p">={</span><span class="n">https</span><span class="p">:</span><span class="c1">//www.irjet.net/archives/V6/i5/IRJET-V6I5318.pdf}, number={5}, journal={International Research Journal of Engineering and Technology (IRJET)}, author={Chauhan, Navan}, year={2019}}</span>
</div>

</code></pre>]]></content:encoded></item><item><guid isPermaLink="true">https://navanchauhan.github.io/posts/hello-world</guid><title>Hello World</title><description>My first post.</description><link>https://navanchauhan.github.io/posts/hello-world</link><pubDate>Tue, 16 Apr 2019 17:39:00 +0530</pubDate><content:encoded><![CDATA[<h1>Hello World</h1><p><strong>Why a Hello World post?</strong></p><p>Just re-did the entire website using Publish (Publish by John Sundell). So, a new hello world post :)</p>]]></content:encoded></item></channel></rss>