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diff --git a/docs/feed.rss b/docs/feed.rss index df334a3..12e9f8d 100644 --- a/docs/feed.rss +++ b/docs/feed.rss @@ -4,8 +4,8 @@ <title>Navan's Archive</title> <description>Rare Tips, Tricks and Posts</description> <link>https://web.navan.dev/</link><language>en</language> - <lastBuildDate>Thu, 21 Mar 2024 13:54:34 -0000</lastBuildDate> - <pubDate>Thu, 21 Mar 2024 13:54:34 -0000</pubDate> + <lastBuildDate>Thu, 21 Mar 2024 14:27:28 -0000</lastBuildDate> + <pubDate>Thu, 21 Mar 2024 14:27:28 -0000</pubDate> <ttl>250</ttl> <atom:link href="https://web.navan.dev/feed.rss" rel="self" type="application/rss+xml"/> @@ -553,18 +553,17 @@ creating<span class="w"> </span>a<span class="w"> </span>DOS<span class="w"> </s <p>Which is equivalent to the general cubic equation:</p> -<p><script type="text/javascript" - src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></p> +<script src="https://cdn.jsdelivr.net/npm/mathjax@4.0.0-beta.4/tex-mml-chtml.js" id="MathJax-script"></script> -</script> +<script src="https://cdn.jsdelivr.net/npm/mathjax@4.0.0-beta.4/input/tex/extensions/noerrors.js" charset="UTF-8"></script> -$$ +<p>$$ y = ax^3 + bx^2 + cx + d -$$ +$$</p> -### Optimizer Selection & Training -<div class="codehilite"> +<h3>Optimizer Selection & Training</h3> +<div class="codehilite"> <pre><span></span><code><span class="n">optimizer</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">keras</span><span class="o">.</span><span class="n">optimizers</span><span class="o">.</span><span class="n">Adam</span><span class="p">(</span><span class="n">learning_rate</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span> <span class="n">num_epochs</span> <span class="o">=</span> <span class="mi">10_000</span> @@ -577,25 +576,23 @@ $$ <span class="k">if</span> <span class="p">(</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="mi">1000</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Epoch: </span><span class="si">{</span><span class="n">epoch</span><span class="o">+</span><span class="mi">1</span><span class="si">}</span><span class="s2">, Loss: </span><span class="si">{</span><span class="n">loss</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span><span class="si">}</span><span class="s2">"</span> </code></pre> - </div> +<p>In TensorFlow 1, we would have been using <code>tf.Session</code> instead. </p> -In TensorFlow 1, we would have been using `tf.Session` instead. +<p>Here we are using <code>GradientTape()</code> instead, to keep track of the loss evaluation and coefficients. This is crucial, as our optimizer needs these gradients to be able to optimize our coefficients. </p> -Here we are using `GradientTape()` instead, to keep track of the loss evaluation and coefficients. This is crucial, as our optimizer needs these gradients to be able to optimize our coefficients. +<p>Our loss function is Mean Squared Error (MSE):</p> -Our loss function is Mean Squared Error (MSE) +<p>$$ += \frac{1}{n} \sum_{i=1}^{n}{(Y_i - \hat{Y_i})^2} +$$</p> -$$ -= \frac{1}{n}\sum_{i=1}^{n} (Y_i - \^{Y_i}) -$$ +<p>Where <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>Y</mi><mi>i</mi></msub><mo stretchy="false" style="math-style:normal;math-depth:0;">^</mo></mover></math> is the predicted value and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Y</mi><mi>i</mi></msub></math> is the actual value</p> -Where $\^{Y_i}$ is the predicted value and $Y_i$ is the actual value +<h3>Plotting Final Coefficients</h3> -### Plotting Final Coefficients <div class="codehilite"> - <pre><span></span><code><span class="n">final_coefficients</span> <span class="o">=</span> <span class="p">[</span><span class="n">c</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">coefficients</span><span class="p">]</span> <span class="nb">print</span><span class="p">(</span><span class="s2">"Final Coefficients:"</span><span class="p">,</span> <span class="n">final_coefficients</span><span class="p">)</span> @@ -606,18 +603,15 @@ Where $\^{Y_i}$ is the predicted value and $Y_i$ is the actual value <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Salary vs Position"</span><span class="p">)</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> </code></pre> - </div> +<h2>Code Snippet for a Polynomial of Degree N</h2> +<h3>Using Gradient Tape</h3> -## Code Snippet for a Polynomial of Degree N - -### Using Gradient Tape +<p>This should work regardless of the Keras backend version (2 or 3)</p> -This should work regardless of the Keras backend version (2 or 3) <div class="codehilite"> - <pre><span></span><code><span class="kn">import</span> <span class="nn">tensorflow</span> <span class="k">as</span> <span class="nn">tf</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> <span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span> @@ -666,17 +660,15 @@ This should work regardless of the Keras backend version (2 or 3) <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> </code></pre> - </div> +<h3>Without Gradient Tape</h3> -### Without Gradient Tape +<p>This relies on the Optimizer's <code>minimize</code> function and uses the <code>var_list</code> parameter to update the variables.</p> -This relies on the Optimizer's `minimize` function and uses the `var_list` parameter to update the variables. +<p>This will not work with Keras 3 backend in TF 2.16.0 and above unless you switch to the legacy backend.</p> -This will not work with Keras 3 backend in TF 2.16.0 and above unless you switch to the legacy backend. <div class="codehilite"> - <pre><span></span><code><span class="kn">import</span> <span class="nn">tensorflow</span> <span class="k">as</span> <span class="nn">tf</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> <span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span> @@ -726,26 +718,24 @@ This will not work with Keras 3 backend in TF 2.16.0 and above unless you switch <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">x_column</span><span class="si">}</span><span class="s2"> vs </span><span class="si">{</span><span class="n">y_column</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span> </code></pre> - </div> +<p>As always, remember to tweak the parameters and choose the correct model for the job. A polynomial regression model might not even be the best model for this particular dataset.</p> +<h2>Further Programming</h2> -As always, remember to tweak the parameters and choose the correct model for the job. A polynomial regression model might not even be the best model for this particular dataset. +<p>How would you modify this code to use another type of nonlinear regression? Say, </p> -## Further Programming +<p>$$ y = ab^x $$</p> -How would you modify this code to use another type of nonlinear regression? Say, $ y = ab^x $ +<p>Hint: Your loss calculation would be similar to:</p> -Hint: Your loss calculation would be similar to: <div class="codehilite"> - <pre><span></span><code><span class="n">bx</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">coefficients</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">X</span><span class="p">)</span> <span class="n">pred_y</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">math</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">coefficients</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">bx</span><span class="p">)</span> <span class="n">loss</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_mean</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">square</span><span class="p">(</span><span class="n">pred_y</span> <span class="o">-</span> <span class="n">Y</span><span class="p">))</span> </code></pre> - -<p></div></p> +</div> ]]></content:encoded> </item> |