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diff --git a/Content/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.md b/Content/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.md new file mode 100644 index 0000000..4341f09 --- /dev/null +++ b/Content/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.md @@ -0,0 +1,241 @@ +--- +date: 2024-03-21 12:46 +description: Predicting n-th degree polynomials using TensorFlow 2.x +tags: Tutorial, Tensorflow, Colab +--- + +# Polynomial Regression Using TensorFlow 2.x + +I have a similar post titled [Polynomial Regression Using Tensorflow](/posts/2019-12-16-TensorFlow-Polynomial-Regression.html) that used `tensorflow.compat.v1` (Which still works as of TF 2.16). But, I thought it would be nicer to redo it with newer TF versions. + +I will be skipping all the introductions about polynomial regression and jumping straight to the code. Personally, I prefer using `scikit-learn` for this task. + +## Position vs Salary Dataset + +Again, we will be using https://drive.google.com/file/d/1tNL4jxZEfpaP4oflfSn6pIHJX7Pachm9/view (Salary vs Position Dataset) + +If you are in a Python Notebook environment like Kaggle or Google Colaboratory, you can simply run: +```Termcap +!wget --no-check-certificate 'https://docs.google.com/uc?export=download&id=1tNL4jxZEfpaP4oflfSn6pIHJX7Pachm9' -O data.csv +``` + +## Code + +If you just want to copy-paste the code, scroll to the bottom for the entire snippet. Here I will try and walk through setting up code for a 3rd-degree (cubic) polynomial + +### Imports + +```python +import pandas as pd +import tensorflow as tf +import matplotlib.pyplot as plt +import numpy as np +``` + +### Reading the Dataset + +```python +df = pd.read_csv("data.csv") +``` + +### Variables and Constants + +Here, we initialize the X and Y values as constants, since they are not going to change. The coefficients are defined as variables. + +```python +X = tf.constant(df["Level"], dtype=tf.float32) +Y = tf.constant(df["Salary"], dtype=tf.float32) + +coefficients = [tf.Variable(np.random.randn() * 0.01, dtype=tf.float32) for _ in range(4)] +``` + +Here, `X` and `Y` are the values from our dataset. We initialize the coefficients for the equations as small random values. + +These coefficients are evaluated by Tensorflow's `tf.math.poyval` function which returns the n-th order polynomial based on how many coefficients are passed. Since our list of coefficients contains 4 different variables, it will be evaluated as: + +``` +y = (x**3)*coefficients[3] + (x**2)*coefficients[2] + (x**1)*coefficients[1] (x**0)*coefficients[0] +``` + +Which is equivalent to the general cubic equation: + +<script type="text/javascript" + src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"> +</script> + +$$ +y = ax^3 + bx^2 + cx + d +$$ + +### Optimizer Selection & Training + +```python +optimizer = tf.keras.optimizers.Adam(learning_rate=0.3) +num_epochs = 10_000 + +for epoch in range(num_epochs): + with tf.GradientTape() as tape: + y_pred = tf.math.polyval(coefficients, X) + loss = tf.reduce_mean(tf.square(y - y_pred)) + grads = tape.gradient(loss, coefficients) + optimizer.apply_gradients(zip(grads, coefficients)) + if (epoch+1) % 1000 == 0: + print(f"Epoch: {epoch+1}, Loss: {loss.numpy()}" +``` + +In TensorFlow 1, we would have been using `tf.Session` instead. + +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. + +Our loss function is Mean Squared Error (MSE) + +$$ += \frac{1}{n}\sum_{i=1}^{n} (Y_i - \^{Y_i}) +$$ + +Where $\^{Y_i}$ is the predicted value and $Y_i$ is the actual value + +### Plotting Final Coefficients + +```python +final_coefficients = [c.numpy() for c in coefficients] +print("Final Coefficients:", final_coefficients) + +plt.plot(df["Level"], df["Salary"], label="Original Data") +plt.plot(df["Level"],[tf.math.polyval(final_coefficients, tf.constant(x, dtype=tf.float32)).numpy() for x in df["Level"]]) +plt.ylabel('Salary') +plt.xlabel('Position') +plt.title("Salary vs Position") +plt.show() +``` + + +## Code Snippet for a Polynomial of Degree N + +### Using Gradient Tape + +This should work regardless of the Keras backend version (2 or 3) + +```python +import tensorflow as tf +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt + +df = pd.read_csv("data.csv") + +############################ +## Change Parameters Here ## +############################ +x_column = "Level" # +y_column = "Salary" # +degree = 2 # +learning_rate = 0.3 # +num_epochs = 25_000 # +############################ + +X = tf.constant(df[x_column], dtype=tf.float32) +Y = tf.constant(df[y_column], dtype=tf.float32) + +coefficients = [tf.Variable(np.random.randn() * 0.01, dtype=tf.float32) for _ in range(degree + 1)] + +optimizer = tf.keras.optimizers.Adam(learning_rate=learning_rate) + +for epoch in range(num_epochs): + with tf.GradientTape() as tape: + y_pred = tf.math.polyval(coefficients, X) + loss = tf.reduce_mean(tf.square(Y - y_pred)) + grads = tape.gradient(loss, coefficients) + optimizer.apply_gradients(zip(grads, coefficients)) + if (epoch+1) % 1000 == 0: + print(f"Epoch: {epoch+1}, Loss: {loss.numpy()}") + +final_coefficients = [c.numpy() for c in coefficients] +print("Final Coefficients:", final_coefficients) + +print("Final Equation:", end=" ") +for i in range(degree+1): + print(f"{final_coefficients[i]} * x^{degree-i}", end=" + " if i < degree else "\n") + +plt.plot(X, Y, label="Original Data") +plt.plot(X,[tf.math.polyval(final_coefficients, tf.constant(x, dtype=tf.float32)).numpy() for x in df[x_column]]), label="Our Poynomial" +plt.ylabel(y_column) +plt.xlabel(x_column) +plt.title(f"{x_column} vs {y_column}") +plt.legend() +plt.show() +``` + +### Without Gradient Tape + +This relies on the Optimizer's `minimize` function and uses the `var_list` parameter to update the variables. + +This will not work with Keras 3 backend in TF 2.16.0 and above unless you switch to the legacy backend. + +```python +import tensorflow as tf +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt + +df = pd.read_csv("data.csv") + +############################ +## Change Parameters Here ## +############################ +x_column = "Level" # +y_column = "Salary" # +degree = 2 # +learning_rate = 0.3 # +num_epochs = 25_000 # +############################ + +X = tf.constant(df[x_column], dtype=tf.float32) +Y = tf.constant(df[y_column], dtype=tf.float32) + +coefficients = [tf.Variable(np.random.randn() * 0.01, dtype=tf.float32) for _ in range(degree + 1)] + +optimizer = tf.keras.optimizers.Adam(learning_rate=learning_rate) + +def loss_function(): + pred_y = tf.math.polyval(coefficients, X) + return tf.reduce_mean(tf.square(pred_y - Y)) + +for epoch in range(num_epochs): + optimizer.minimize(loss_function, var_list=coefficients) + if (epoch+1) % 1000 == 0: + current_loss = loss_function().numpy() + print(f"Epoch {epoch+1}: Training Loss: {current_loss}") + +final_coefficients = coefficients.numpy() +print("Final Coefficients:", final_coefficients) + +print("Final Equation:", end=" ") +for i in range(degree+1): + print(f"{final_coefficients[i]} * x^{degree-i}", end=" + " if i < degree else "\n") + +plt.plot(X, Y, label="Original Data") +plt.plot(X,[tf.math.polyval(final_coefficients, tf.constant(x, dtype=tf.float32)).numpy() for x in df[x_column]], label="Our Polynomial") +plt.ylabel(y_column) +plt.xlabel(x_column) +plt.legend() +plt.title(f"{x_column} vs {y_column}") +plt.show() +``` + + +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. + +## Further Programming + +How would you modify this code to use another type of nonlinear regression? Say, $ y = ab^x $ + +Hint: Your loss calculation would be similar to: + +```python +bx = tf.pow(coefficients[1], X) +pred_y = tf.math.multiply(coefficients[0], bx) +loss = tf.reduce_mean(tf.square(pred_y - Y)) +``` + + diff --git a/Resources/images/opengraph/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.png b/Resources/images/opengraph/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.png Binary files differnew file mode 100644 index 0000000..0dbdd08 --- /dev/null +++ b/Resources/images/opengraph/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.png diff --git a/docs/feed.rss b/docs/feed.rss index d242684..df334a3 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>Fri, 15 Mar 2024 15:00:25 -0000</lastBuildDate> - <pubDate>Fri, 15 Mar 2024 15:00:25 -0000</pubDate> + <lastBuildDate>Thu, 21 Mar 2024 13:54:34 -0000</lastBuildDate> + <pubDate>Thu, 21 Mar 2024 13:54:34 -0000</pubDate> <ttl>250</ttl> <atom:link href="https://web.navan.dev/feed.rss" rel="self" type="application/rss+xml"/> @@ -484,6 +484,273 @@ creating<span class="w"> </span>a<span class="w"> </span>DOS<span class="w"> </s <item> <guid isPermaLink="true"> + https://web.navan.dev/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html + </guid> + <title> + Polynomial Regression Using TensorFlow 2.x + </title> + <description> + Predicting n-th degree polynomials using TensorFlow 2.x + </description> + <link>https://web.navan.dev/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html</link> + <pubDate>Thu, 21 Mar 2024 12:46:00 -0000</pubDate> + <content:encoded><![CDATA[<h1>Polynomial Regression Using TensorFlow 2.x</h1> + +<p>I have a similar post titled <a rel="noopener" target="_blank" href="/posts/2019-12-16-TensorFlow-Polynomial-Regression.html">Polynomial Regression Using Tensorflow</a> that used <code>tensorflow.compat.v1</code> (Which still works as of TF 2.16). But, I thought it would be nicer to redo it with newer TF versions. </p> + +<p>I will be skipping all the introductions about polynomial regression and jumping straight to the code. Personally, I prefer using <code>scikit-learn</code> for this task.</p> + +<h2>Position vs Salary Dataset</h2> + +<p>Again, we will be using https://drive.google.com/file/d/1tNL4jxZEfpaP4oflfSn6pIHJX7Pachm9/view (Salary vs Position Dataset)</p> + +<p>If you are in a Python Notebook environment like Kaggle or Google Colaboratory, you can simply run:</p> + +<div class="codehilite"> +<pre><span></span><code><span class="nt">!wget</span><span class="na"> --no-check-certificate 'https</span><span class="p">:</span><span class="nc">//docs.google.com/uc?export</span><span class="o">=</span><span class="l">download&id=1tNL4jxZEfpaP4oflfSn6pIHJX7Pachm9' -O data.csv</span> +</code></pre> +</div> + +<h2>Code</h2> + +<p>If you just want to copy-paste the code, scroll to the bottom for the entire snippet. Here I will try and walk through setting up code for a 3rd-degree (cubic) polynomial</p> + +<h3>Imports</h3> + +<div class="codehilite"> +<pre><span></span><code><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span> +<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">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span> +<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> +</code></pre> +</div> + +<h3>Reading the Dataset</h3> + +<div class="codehilite"> +<pre><span></span><code><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">"data.csv"</span><span class="p">)</span> +</code></pre> +</div> + +<h3>Variables and Constants</h3> + +<p>Here, we initialize the X and Y values as constants, since they are not going to change. The coefficients are defined as variables.</p> + +<div class="codehilite"> +<pre><span></span><code><span class="n">X</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="s2">"Level"</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</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">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="s2">"Salary"</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> + +<span class="n">coefficients</span> <span class="o">=</span> <span class="p">[</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="o">*</span> <span class="mf">0.01</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">)]</span> +</code></pre> +</div> + +<p>Here, <code>X</code> and <code>Y</code> are the values from our dataset. We initialize the coefficients for the equations as small random values.</p> + +<p>These coefficients are evaluated by Tensorflow's <code>tf.math.poyval</code> function which returns the n-th order polynomial based on how many coefficients are passed. Since our list of coefficients contains 4 different variables, it will be evaluated as:</p> + +<pre><code>y = (x**3)*coefficients[3] + (x**2)*coefficients[2] + (x**1)*coefficients[1] (x**0)*coefficients[0] +</code></pre> + +<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> + +$$ +y = ax^3 + bx^2 + cx + d +$$ + +### Optimizer Selection & Training +<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> + +<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">num_epochs</span><span class="p">):</span> + <span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">GradientTape</span><span class="p">()</span> <span class="k">as</span> <span class="n">tape</span><span class="p">:</span> + <span class="n">y_pred</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">polyval</span><span class="p">(</span><span class="n">coefficients</span><span class="p">,</span> <span class="n">X</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">y</span> <span class="o">-</span> <span class="n">y_pred</span><span class="p">))</span> + <span class="n">grads</span> <span class="o">=</span> <span class="n">tape</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">coefficients</span><span class="p">)</span> + <span class="n">optimizer</span><span class="o">.</span><span class="n">apply_gradients</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">grads</span><span class="p">,</span> <span class="n">coefficients</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="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> + + +In TensorFlow 1, we would have been using `tf.Session` instead. + +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. + +Our loss function is Mean Squared Error (MSE) + +$$ += \frac{1}{n}\sum_{i=1}^{n} (Y_i - \^{Y_i}) +$$ + +Where $\^{Y_i}$ is the predicted value and $Y_i$ is the actual value + +### 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> + +<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="s2">"Level"</span><span class="p">],</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Salary"</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Original Data"</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">df</span><span class="p">[</span><span class="s2">"Level"</span><span class="p">],[</span><span class="n">tf</span><span class="o">.</span><span class="n">math</span><span class="o">.</span><span class="n">polyval</span><span class="p">(</span><span class="n">final_coefficients</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">))</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Level"</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">'Salary'</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">'Position'</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">"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> + + + +## Code Snippet for a Polynomial of Degree N + +### Using Gradient Tape + +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> +<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</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">"data.csv"</span><span class="p">)</span> + +<span class="c1">############################</span> +<span class="c1">## Change Parameters Here ##</span> +<span class="c1">############################</span> +<span class="n">x_column</span> <span class="o">=</span> <span class="s2">"Level"</span> <span class="c1">#</span> +<span class="n">y_column</span> <span class="o">=</span> <span class="s2">"Salary"</span> <span class="c1">#</span> +<span class="n">degree</span> <span class="o">=</span> <span class="mi">2</span> <span class="c1">#</span> +<span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="c1">#</span> +<span class="n">num_epochs</span> <span class="o">=</span> <span class="mi">25_000</span> <span class="c1">#</span> +<span class="c1">############################</span> + +<span class="n">X</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="n">x_column</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</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">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="n">y_column</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> + +<span class="n">coefficients</span> <span class="o">=</span> <span class="p">[</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="o">*</span> <span class="mf">0.01</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">degree</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span> + +<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="n">learning_rate</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">num_epochs</span><span class="p">):</span> + <span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">GradientTape</span><span class="p">()</span> <span class="k">as</span> <span class="n">tape</span><span class="p">:</span> + <span class="n">y_pred</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">polyval</span><span class="p">(</span><span class="n">coefficients</span><span class="p">,</span> <span class="n">X</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">Y</span> <span class="o">-</span> <span class="n">y_pred</span><span class="p">))</span> + <span class="n">grads</span> <span class="o">=</span> <span class="n">tape</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">coefficients</span><span class="p">)</span> + <span class="n">optimizer</span><span class="o">.</span><span class="n">apply_gradients</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">grads</span><span class="p">,</span> <span class="n">coefficients</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="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><span class="p">)</span> + +<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> + +<span class="nb">print</span><span class="p">(</span><span class="s2">"Final Equation:"</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">" "</span><span class="p">)</span> +<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">degree</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span> + <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">final_coefficients</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s2"> * x^</span><span class="si">{</span><span class="n">degree</span><span class="o">-</span><span class="n">i</span><span class="si">}</span><span class="s2">"</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">" + "</span> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="n">degree</span> <span class="k">else</span> <span class="s2">"</span><span class="se">\n</span><span class="s2">"</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">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Original Data"</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">X</span><span class="p">,[</span><span class="n">tf</span><span class="o">.</span><span class="n">math</span><span class="o">.</span><span class="n">polyval</span><span class="p">(</span><span class="n">final_coefficients</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">))</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">df</span><span class="p">[</span><span class="n">x_column</span><span class="p">]]),</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Our Poynomial"</span> +<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="n">y_column</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="n">x_column</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="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">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> + + +### Without Gradient Tape + +This relies on the Optimizer's `minimize` function and uses the `var_list` parameter to update the variables. + +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> +<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</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">"data.csv"</span><span class="p">)</span> + +<span class="c1">############################</span> +<span class="c1">## Change Parameters Here ##</span> +<span class="c1">############################</span> +<span class="n">x_column</span> <span class="o">=</span> <span class="s2">"Level"</span> <span class="c1">#</span> +<span class="n">y_column</span> <span class="o">=</span> <span class="s2">"Salary"</span> <span class="c1">#</span> +<span class="n">degree</span> <span class="o">=</span> <span class="mi">2</span> <span class="c1">#</span> +<span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="c1">#</span> +<span class="n">num_epochs</span> <span class="o">=</span> <span class="mi">25_000</span> <span class="c1">#</span> +<span class="c1">############################</span> + +<span class="n">X</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="n">x_column</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</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">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="n">y_column</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> + +<span class="n">coefficients</span> <span class="o">=</span> <span class="p">[</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="o">*</span> <span class="mf">0.01</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">degree</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span> + +<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="n">learning_rate</span><span class="p">)</span> + +<span class="k">def</span> <span class="nf">loss_function</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">polyval</span><span class="p">(</span><span class="n">coefficients</span><span class="p">,</span> <span class="n">X</span><span class="p">)</span> + <span class="k">return</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> + +<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">num_epochs</span><span class="p">):</span> + <span class="n">optimizer</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">loss_function</span><span class="p">,</span> <span class="n">var_list</span><span class="o">=</span><span class="n">coefficients</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">current_loss</span> <span class="o">=</span> <span class="n">loss_function</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</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">: Training Loss: </span><span class="si">{</span><span class="n">current_loss</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span> + +<span class="n">final_coefficients</span> <span class="o">=</span> <span class="n">coefficients</span><span class="o">.</span><span class="n">numpy</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> + +<span class="nb">print</span><span class="p">(</span><span class="s2">"Final Equation:"</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">" "</span><span class="p">)</span> +<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">degree</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span> + <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">final_coefficients</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s2"> * x^</span><span class="si">{</span><span class="n">degree</span><span class="o">-</span><span class="n">i</span><span class="si">}</span><span class="s2">"</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">" + "</span> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="n">degree</span> <span class="k">else</span> <span class="s2">"</span><span class="se">\n</span><span class="s2">"</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">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Original Data"</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">X</span><span class="p">,[</span><span class="n">tf</span><span class="o">.</span><span class="n">math</span><span class="o">.</span><span class="n">polyval</span><span class="p">(</span><span class="n">final_coefficients</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">))</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">df</span><span class="p">[</span><span class="n">x_column</span><span class="p">]],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Our Polynomial"</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="n">y_column</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="n">x_column</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">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> + + + +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. + +## Further Programming + +How would you modify this code to use another type of nonlinear regression? Say, $ y = ab^x $ + +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> +]]></content:encoded> + </item> + + <item> + <guid isPermaLink="true"> https://web.navan.dev/posts/hello-world.html </guid> <title> diff --git a/docs/images/opengraph/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.png b/docs/images/opengraph/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.png Binary files differnew file mode 100644 index 0000000..0dbdd08 --- /dev/null +++ b/docs/images/opengraph/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.png diff --git a/docs/index.html b/docs/index.html index f6a4942..0a3070a 100644 --- a/docs/index.html +++ b/docs/index.html @@ -50,6 +50,21 @@ <h2>Recent Posts</h2> <ul> + <li><a href="/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html">Polynomial Regression Using TensorFlow 2.x</a></li> + <ul> + <li>Predicting n-th degree polynomials using TensorFlow 2.x</li> + <li>Published On: 2024-03-21 12:46</li> + <li>Tags: + + <a href='/tags/Tutorial.html'>Tutorial</a>, + + <a href='/tags/Tensorflow.html'>Tensorflow</a>, + + <a href='/tags/Colab.html'>Colab</a> + + </ul> + + <li><a href="/posts/2024-03-15-setting-up-macos-for-8088-dos-dev.html">Cross-Compiling Hello World for DOS on macOS</a></li> <ul> <li>This goes through compiling Open Watcom 2 and creating simple hello-world exampls</li> @@ -104,19 +119,6 @@ </ul> - 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But, I thought it would be nicer to redo it with newer TF versions. </p> + +<p>I will be skipping all the introductions about polynomial regression and jumping straight to the code. Personally, I prefer using <code>scikit-learn</code> for this task.</p> + +<h2>Position vs Salary Dataset</h2> + +<p>Again, we will be using https://drive.google.com/file/d/1tNL4jxZEfpaP4oflfSn6pIHJX7Pachm9/view (Salary vs Position Dataset)</p> + +<p>If you are in a Python Notebook environment like Kaggle or Google Colaboratory, you can simply run:</p> + +<div class="codehilite"> +<pre><span></span><code><span class="nt">!wget</span><span class="na"> --no-check-certificate 'https</span><span class="p">:</span><span class="nc">//docs.google.com/uc?export</span><span class="o">=</span><span class="l">download&id=1tNL4jxZEfpaP4oflfSn6pIHJX7Pachm9' -O data.csv</span> +</code></pre> +</div> + +<h2>Code</h2> + +<p>If you just want to copy-paste the code, scroll to the bottom for the entire snippet. Here I will try and walk through setting up code for a 3rd-degree (cubic) polynomial</p> + +<h3>Imports</h3> + +<div class="codehilite"> +<pre><span></span><code><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span> +<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">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span> +<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> +</code></pre> +</div> + +<h3>Reading the Dataset</h3> + +<div class="codehilite"> +<pre><span></span><code><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">"data.csv"</span><span class="p">)</span> +</code></pre> +</div> + +<h3>Variables and Constants</h3> + +<p>Here, we initialize the X and Y values as constants, since they are not going to change. The coefficients are defined as variables.</p> + +<div class="codehilite"> +<pre><span></span><code><span class="n">X</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="s2">"Level"</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</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">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="s2">"Salary"</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> + +<span class="n">coefficients</span> <span class="o">=</span> <span class="p">[</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="o">*</span> <span class="mf">0.01</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">)]</span> +</code></pre> +</div> + +<p>Here, <code>X</code> and <code>Y</code> are the values from our dataset. We initialize the coefficients for the equations as small random values.</p> + +<p>These coefficients are evaluated by Tensorflow's <code>tf.math.poyval</code> function which returns the n-th order polynomial based on how many coefficients are passed. Since our list of coefficients contains 4 different variables, it will be evaluated as:</p> + +<pre><code>y = (x**3)*coefficients[3] + (x**2)*coefficients[2] + (x**1)*coefficients[1] (x**0)*coefficients[0] +</code></pre> + +<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> + +$$ +y = ax^3 + bx^2 + cx + d +$$ + +### Optimizer Selection & Training +<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> + +<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">num_epochs</span><span class="p">):</span> + <span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">GradientTape</span><span class="p">()</span> <span class="k">as</span> <span class="n">tape</span><span class="p">:</span> + <span class="n">y_pred</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">polyval</span><span class="p">(</span><span class="n">coefficients</span><span class="p">,</span> <span class="n">X</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">y</span> <span class="o">-</span> <span class="n">y_pred</span><span class="p">))</span> + <span class="n">grads</span> <span class="o">=</span> <span class="n">tape</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">coefficients</span><span class="p">)</span> + <span class="n">optimizer</span><span class="o">.</span><span class="n">apply_gradients</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">grads</span><span class="p">,</span> <span class="n">coefficients</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="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> + + +In TensorFlow 1, we would have been using `tf.Session` instead. + +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. + +Our loss function is Mean Squared Error (MSE) + +$$ += \frac{1}{n}\sum_{i=1}^{n} (Y_i - \^{Y_i}) +$$ + +Where $\^{Y_i}$ is the predicted value and $Y_i$ is the actual value + +### 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> + +<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="s2">"Level"</span><span class="p">],</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Salary"</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Original Data"</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">df</span><span class="p">[</span><span class="s2">"Level"</span><span class="p">],[</span><span class="n">tf</span><span class="o">.</span><span class="n">math</span><span class="o">.</span><span class="n">polyval</span><span class="p">(</span><span class="n">final_coefficients</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">))</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Level"</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">'Salary'</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">'Position'</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">"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> + + + +## Code Snippet for a Polynomial of Degree N + +### Using Gradient Tape + +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> +<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</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">"data.csv"</span><span class="p">)</span> + +<span class="c1">############################</span> +<span class="c1">## Change Parameters Here ##</span> +<span class="c1">############################</span> +<span class="n">x_column</span> <span class="o">=</span> <span class="s2">"Level"</span> <span class="c1">#</span> +<span class="n">y_column</span> <span class="o">=</span> <span class="s2">"Salary"</span> <span class="c1">#</span> +<span class="n">degree</span> <span class="o">=</span> <span class="mi">2</span> <span class="c1">#</span> +<span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="c1">#</span> +<span class="n">num_epochs</span> <span class="o">=</span> <span class="mi">25_000</span> <span class="c1">#</span> +<span class="c1">############################</span> + +<span class="n">X</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="n">x_column</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</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">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="n">y_column</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> + +<span class="n">coefficients</span> <span class="o">=</span> <span class="p">[</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="o">*</span> <span class="mf">0.01</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">degree</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span> + +<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="n">learning_rate</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">num_epochs</span><span class="p">):</span> + <span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">GradientTape</span><span class="p">()</span> <span class="k">as</span> <span class="n">tape</span><span class="p">:</span> + <span class="n">y_pred</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">polyval</span><span class="p">(</span><span class="n">coefficients</span><span class="p">,</span> <span class="n">X</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">Y</span> <span class="o">-</span> <span class="n">y_pred</span><span class="p">))</span> + <span class="n">grads</span> <span class="o">=</span> <span class="n">tape</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">coefficients</span><span class="p">)</span> + <span class="n">optimizer</span><span class="o">.</span><span class="n">apply_gradients</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">grads</span><span class="p">,</span> <span class="n">coefficients</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="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><span class="p">)</span> + +<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> + +<span class="nb">print</span><span class="p">(</span><span class="s2">"Final Equation:"</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">" "</span><span class="p">)</span> +<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">degree</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span> + <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">final_coefficients</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s2"> * x^</span><span class="si">{</span><span class="n">degree</span><span class="o">-</span><span class="n">i</span><span class="si">}</span><span class="s2">"</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">" + "</span> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="n">degree</span> <span class="k">else</span> <span class="s2">"</span><span class="se">\n</span><span class="s2">"</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">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Original Data"</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">X</span><span class="p">,[</span><span class="n">tf</span><span class="o">.</span><span class="n">math</span><span class="o">.</span><span class="n">polyval</span><span class="p">(</span><span class="n">final_coefficients</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">))</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">df</span><span class="p">[</span><span class="n">x_column</span><span class="p">]]),</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Our Poynomial"</span> +<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="n">y_column</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="n">x_column</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="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">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> + + +### Without Gradient Tape + +This relies on the Optimizer's `minimize` function and uses the `var_list` parameter to update the variables. + +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> +<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</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">"data.csv"</span><span class="p">)</span> + +<span class="c1">############################</span> +<span class="c1">## Change Parameters Here ##</span> +<span class="c1">############################</span> +<span class="n">x_column</span> <span class="o">=</span> <span class="s2">"Level"</span> <span class="c1">#</span> +<span class="n">y_column</span> <span class="o">=</span> <span class="s2">"Salary"</span> <span class="c1">#</span> +<span class="n">degree</span> <span class="o">=</span> <span class="mi">2</span> <span class="c1">#</span> +<span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">0.3</span> <span class="c1">#</span> +<span class="n">num_epochs</span> <span class="o">=</span> <span class="mi">25_000</span> <span class="c1">#</span> +<span class="c1">############################</span> + +<span class="n">X</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="n">x_column</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</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">constant</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="n">y_column</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> + +<span class="n">coefficients</span> <span class="o">=</span> <span class="p">[</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="o">*</span> <span class="mf">0.01</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">degree</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span> + +<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="n">learning_rate</span><span class="p">)</span> + +<span class="k">def</span> <span class="nf">loss_function</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">polyval</span><span class="p">(</span><span class="n">coefficients</span><span class="p">,</span> <span class="n">X</span><span class="p">)</span> + <span class="k">return</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> + +<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">num_epochs</span><span class="p">):</span> + <span class="n">optimizer</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">loss_function</span><span class="p">,</span> <span class="n">var_list</span><span class="o">=</span><span class="n">coefficients</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">current_loss</span> <span class="o">=</span> <span class="n">loss_function</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</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">: Training Loss: </span><span class="si">{</span><span class="n">current_loss</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span> + +<span class="n">final_coefficients</span> <span class="o">=</span> <span class="n">coefficients</span><span class="o">.</span><span class="n">numpy</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> + +<span class="nb">print</span><span class="p">(</span><span class="s2">"Final Equation:"</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">" "</span><span class="p">)</span> +<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">degree</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span> + <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">final_coefficients</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="si">}</span><span class="s2"> * x^</span><span class="si">{</span><span class="n">degree</span><span class="o">-</span><span class="n">i</span><span class="si">}</span><span class="s2">"</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">" + "</span> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="n">degree</span> <span class="k">else</span> <span class="s2">"</span><span class="se">\n</span><span class="s2">"</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">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Original Data"</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">X</span><span class="p">,[</span><span class="n">tf</span><span class="o">.</span><span class="n">math</span><span class="o">.</span><span class="n">polyval</span><span class="p">(</span><span class="n">final_coefficients</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">))</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">df</span><span class="p">[</span><span class="n">x_column</span><span class="p">]],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Our Polynomial"</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="n">y_column</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="n">x_column</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">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> + + + +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. + +## Further Programming + +How would you modify this code to use another type of nonlinear regression? Say, $ y = ab^x $ + +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> + + <blockquote>If you have scrolled this far, consider subscribing to my mailing list <a href="https://listmonk.navan.dev/subscription/form">here.</a> You can subscribe to either a specific type of post you are interested in, or subscribe to everything with the "Everything" list.</blockquote> + <script data-isso="https://comments.navan.dev/" + src="https://comments.navan.dev/js/embed.min.js"></script> + <section id="isso-thread"> + <noscript>Javascript needs to be activated to view comments.</noscript> + </section> +</main> + + <script src="assets/manup.min.js"></script> + <script src="/pwabuilder-sw-register.js"></script> +</body> +</html>
\ No newline at end of file diff --git a/docs/posts/index.html b/docs/posts/index.html index 2d9d613..d886b19 100644 --- a/docs/posts/index.html +++ b/docs/posts/index.html @@ -52,6 +52,21 @@ <ul> + <li><a href="/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html">Polynomial Regression Using TensorFlow 2.x</a></li> + <ul> + <li>Predicting n-th degree polynomials using TensorFlow 2.x</li> + <li>Published On: 2024-03-21 12:46</li> + <li>Tags: + + <a href='/tags/Tutorial.html'>Tutorial</a>, + + <a href='/tags/Tensorflow.html'>Tensorflow</a>, + + <a href='/tags/Colab.html'>Colab</a> + + </ul> + + <li><a href="/posts/2024-03-15-setting-up-macos-for-8088-dos-dev.html">Cross-Compiling Hello World for DOS on macOS</a></li> <ul> <li>This goes through compiling Open Watcom 2 and creating simple hello-world exampls</li> diff --git a/docs/tags/Colab.html b/docs/tags/Colab.html index a3721a7..fd8ef08 100644 --- a/docs/tags/Colab.html +++ b/docs/tags/Colab.html @@ -49,6 +49,21 @@ <ul> + <li><a href="/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html">Polynomial Regression Using TensorFlow 2.x</a></li> + <ul> + <li>Predicting n-th degree polynomials using TensorFlow 2.x</li> + <li>Published On: 2024-03-21 12:46</li> + <li>Tags: + + <a href='/tags/Tutorial.html'>Tutorial</a>, + + <a href='/tags/Tensorflow.html'>Tensorflow</a>, + + <a href='/tags/Colab.html'>Colab</a> + + </ul> + + <li><a href="/posts/2020-07-01-Install-rdkit-colab.html">Installing RDKit on Google Colab</a></li> <ul> <li>Install RDKit on Google Colab with one code snippet.</li> diff --git a/docs/tags/Tensorflow.html b/docs/tags/Tensorflow.html index 3bcb911..04006bb 100644 --- a/docs/tags/Tensorflow.html +++ b/docs/tags/Tensorflow.html @@ -49,6 +49,21 @@ <ul> + <li><a href="/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.html">Polynomial Regression Using TensorFlow 2.x</a></li> + <ul> + <li>Predicting n-th degree polynomials using TensorFlow 2.x</li> + <li>Published On: 2024-03-21 12:46</li> + <li>Tags: + + <a href='/tags/Tutorial.html'>Tutorial</a>, + + <a href='/tags/Tensorflow.html'>Tensorflow</a>, + + <a href='/tags/Colab.html'>Colab</a> + + </ul> + + <li><a href="/posts/2019-12-16-TensorFlow-Polynomial-Regression.html">Polynomial Regression Using TensorFlow</a></li> <ul> <li>Polynomial regression using TensorFlow</li> |
