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Diffstat (limited to 'Content')
| -rw-r--r-- | Content/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.md | 17 |
1 files changed, 9 insertions, 8 deletions
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 index 4341f09..6317175 100644 --- a/Content/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.md +++ b/Content/posts/2024-03-21-Polynomial-Regression-in-TensorFlow-2.md @@ -59,9 +59,8 @@ y = (x**3)*coefficients[3] + (x**2)*coefficients[2] + (x**1)*coefficients[1] (x* 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> +<script src="https://cdn.jsdelivr.net/npm/mathjax@4.0.0-beta.4/tex-mml-chtml.js" id="MathJax-script"></script> +<script src="https://cdn.jsdelivr.net/npm/mathjax@4.0.0-beta.4/input/tex/extensions/noerrors.js" charset="UTF-8"></script> $$ y = ax^3 + bx^2 + cx + d @@ -85,15 +84,15 @@ for epoch in range(num_epochs): In TensorFlow 1, we would have been using `tf.Session` instead. -Here we are using `GradientTape()` instead, to keep track of the loss evaluation and coefficients. This is crucial, as our optimizer needs these gradients to be able to optimize our coefficients. +Here we are using `GradientTape()` instead, to keep track of the loss evaluation and coefficients. This is crucial, as our optimizer needs these gradients to be able to optimize our coefficients. -Our loss function is Mean Squared Error (MSE) +Our loss function is Mean Squared Error (MSE): $$ -= \frac{1}{n}\sum_{i=1}^{n} (Y_i - \^{Y_i}) += \frac{1}{n} \sum_{i=1}^{n}{(Y\_i - \hat{Y\_i})^2} $$ -Where $\^{Y_i}$ is the predicted value and $Y_i$ is the actual value +Where <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>Y</mi><mi>i</mi></msub><mo stretchy="false" style="math-style:normal;math-depth:0;">^</mo></mover></math> is the predicted value and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>Y</mi><mi>i</mi></msub></math> is the actual value ### Plotting Final Coefficients @@ -228,7 +227,9 @@ As always, remember to tweak the parameters and choose the correct model for the ## Further Programming -How would you modify this code to use another type of nonlinear regression? Say, $ y = ab^x $ +How would you modify this code to use another type of nonlinear regression? Say, + +$$ y = ab^x $$ Hint: Your loss calculation would be similar to: |