added tensorflow
This commit is contained in:
mhjensen
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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None,
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'___sec47'),
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('scikit-learn implementation', 2, None, '___sec48'),
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('And then with Tensorflow', 2, None, '___sec49')]}
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('Building neural networks in Tensorflow and Keras',
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2,
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None,
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'___sec49'),
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('Tensorflow', 2, None, '___sec50'),
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('Collect and pre-process data', 2, None, '___sec51'),
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('Using TensorFlow backend', 2, None, '___sec52'),
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('Optimizing and using gradient descent', 2, None, '___sec53'),
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('Using Keras', 2, None, '___sec54')]}
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end of tocinfo -->
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<body>
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@@ -202,7 +210,12 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
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</ul>
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</li>
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@@ -261,7 +274,7 @@ MathJax.Hub.Config({
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<li><a href="._NeuralNet-bs008.html">9</a></li>
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<li><a href="._NeuralNet-bs009.html">10</a></li>
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<li><a href="">...</a></li>
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<li><a href="._NeuralNet-bs050.html">51</a></li>
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<li><a href="._NeuralNet-bs055.html">56</a></li>
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<li><a href="._NeuralNet-bs001.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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None,
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'___sec47'),
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('scikit-learn implementation', 2, None, '___sec48'),
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('And then with Tensorflow', 2, None, '___sec49')]}
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('Building neural networks in Tensorflow and Keras',
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2,
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None,
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'___sec49'),
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('Tensorflow', 2, None, '___sec50'),
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('Collect and pre-process data', 2, None, '___sec51'),
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('Using TensorFlow backend', 2, None, '___sec52'),
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('Optimizing and using gradient descent', 2, None, '___sec53'),
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('Using Keras', 2, None, '___sec54')]}
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end of tocinfo -->
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<body>
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@@ -202,7 +210,12 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
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</ul>
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</li>
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@@ -246,7 +259,7 @@ a weight variable.
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<li><a href="._NeuralNet-bs009.html">10</a></li>
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<li><a href="._NeuralNet-bs010.html">11</a></li>
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<li><a href="">...</a></li>
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<li><a href="._NeuralNet-bs050.html">51</a></li>
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<li><a href="._NeuralNet-bs055.html">56</a></li>
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<li><a href="._NeuralNet-bs002.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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None,
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'___sec47'),
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('scikit-learn implementation', 2, None, '___sec48'),
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('And then with Tensorflow', 2, None, '___sec49')]}
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('Building neural networks in Tensorflow and Keras',
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2,
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None,
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'___sec49'),
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('Tensorflow', 2, None, '___sec50'),
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('Collect and pre-process data', 2, None, '___sec51'),
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('Using TensorFlow backend', 2, None, '___sec52'),
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('Optimizing and using gradient descent', 2, None, '___sec53'),
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('Using Keras', 2, None, '___sec54')]}
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end of tocinfo -->
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<body>
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@@ -202,7 +210,12 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
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</ul>
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</li>
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@@ -296,7 +309,7 @@ humanities to life science and medicine.
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<li><a href="._NeuralNet-bs010.html">11</a></li>
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<li><a href="._NeuralNet-bs011.html">12</a></li>
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<li><a href="">...</a></li>
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<li><a href="._NeuralNet-bs050.html">51</a></li>
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<li><a href="._NeuralNet-bs055.html">56</a></li>
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<li><a href="._NeuralNet-bs003.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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None,
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'___sec47'),
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('scikit-learn implementation', 2, None, '___sec48'),
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('And then with Tensorflow', 2, None, '___sec49')]}
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('Building neural networks in Tensorflow and Keras',
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2,
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None,
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'___sec49'),
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('Tensorflow', 2, None, '___sec50'),
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('Collect and pre-process data', 2, None, '___sec51'),
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('Using TensorFlow backend', 2, None, '___sec52'),
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('Optimizing and using gradient descent', 2, None, '___sec53'),
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('Using Keras', 2, None, '___sec54')]}
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end of tocinfo -->
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<body>
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@@ -202,7 +210,12 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
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</ul>
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</li>
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@@ -261,7 +274,7 @@ methods we discussed earlier.
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<li><a href="._NeuralNet-bs011.html">12</a></li>
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<li><a href="._NeuralNet-bs012.html">13</a></li>
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<li><a href="">...</a></li>
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<li><a href="._NeuralNet-bs050.html">51</a></li>
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<li><a href="._NeuralNet-bs055.html">56</a></li>
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<li><a href="._NeuralNet-bs004.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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None,
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'___sec47'),
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('scikit-learn implementation', 2, None, '___sec48'),
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('And then with Tensorflow', 2, None, '___sec49')]}
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('Building neural networks in Tensorflow and Keras',
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2,
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None,
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'___sec49'),
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('Tensorflow', 2, None, '___sec50'),
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('Collect and pre-process data', 2, None, '___sec51'),
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('Using TensorFlow backend', 2, None, '___sec52'),
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('Optimizing and using gradient descent', 2, None, '___sec53'),
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('Using Keras', 2, None, '___sec54')]}
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end of tocinfo -->
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<body>
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@@ -202,7 +210,12 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
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</ul>
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</li>
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@@ -253,7 +266,7 @@ to <em>all</em> nodes in the subsequent layer, making this a so-called
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<li><a href="._NeuralNet-bs012.html">13</a></li>
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<li><a href="._NeuralNet-bs013.html">14</a></li>
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<li><a href="">...</a></li>
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<li><a href="._NeuralNet-bs050.html">51</a></li>
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<li><a href="._NeuralNet-bs055.html">56</a></li>
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<li><a href="._NeuralNet-bs005.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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None,
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'___sec47'),
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('scikit-learn implementation', 2, None, '___sec48'),
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('And then with Tensorflow', 2, None, '___sec49')]}
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('Building neural networks in Tensorflow and Keras',
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2,
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None,
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'___sec49'),
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('Tensorflow', 2, None, '___sec50'),
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('Collect and pre-process data', 2, None, '___sec51'),
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('Using TensorFlow backend', 2, None, '___sec52'),
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('Optimizing and using gradient descent', 2, None, '___sec53'),
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('Using Keras', 2, None, '___sec54')]}
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end of tocinfo -->
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<body>
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@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
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</ul>
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</li>
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@@ -262,7 +275,7 @@ recognition.
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<li><a href="._NeuralNet-bs013.html">14</a></li>
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<li><a href="._NeuralNet-bs014.html">15</a></li>
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<li><a href="">...</a></li>
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<li><a href="._NeuralNet-bs050.html">51</a></li>
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<li><a href="._NeuralNet-bs055.html">56</a></li>
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<li><a href="._NeuralNet-bs006.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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None,
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'___sec47'),
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('scikit-learn implementation', 2, None, '___sec48'),
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('And then with Tensorflow', 2, None, '___sec49')]}
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('Building neural networks in Tensorflow and Keras',
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2,
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None,
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'___sec49'),
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('Tensorflow', 2, None, '___sec50'),
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('Collect and pre-process data', 2, None, '___sec51'),
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('Using TensorFlow backend', 2, None, '___sec52'),
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('Optimizing and using gradient descent', 2, None, '___sec53'),
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('Using Keras', 2, None, '___sec54')]}
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end of tocinfo -->
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<body>
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@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
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</ul>
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</li>
|
||||
@@ -254,7 +267,7 @@ especially well-suited for handwriting and speech recognition.
|
||||
<li><a href="._NeuralNet-bs014.html">15</a></li>
|
||||
<li><a href="._NeuralNet-bs015.html">16</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs007.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -255,7 +268,7 @@ type of NN due the unusual activation functions.
|
||||
<li><a href="._NeuralNet-bs015.html">16</a></li>
|
||||
<li><a href="._NeuralNet-bs016.html">17</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs008.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -253,7 +266,7 @@ Such networks are often called <em>multilayer perceptrons</em> (MLPs).
|
||||
<li><a href="._NeuralNet-bs016.html">17</a></li>
|
||||
<li><a href="._NeuralNet-bs017.html">18</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs009.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -258,7 +271,7 @@ as to not restrict the range of output values.
|
||||
<li><a href="._NeuralNet-bs017.html">18</a></li>
|
||||
<li><a href="._NeuralNet-bs018.html">19</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs010.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -259,7 +272,7 @@ of the outputs of <em>all</em> neurons in the previous layer.
|
||||
<li><a href="._NeuralNet-bs018.html">19</a></li>
|
||||
<li><a href="._NeuralNet-bs019.html">20</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs011.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -288,7 +301,7 @@ is obtained.
|
||||
<li><a href="._NeuralNet-bs019.html">20</a></li>
|
||||
<li><a href="._NeuralNet-bs020.html">21</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs012.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -270,7 +283,7 @@ $$
|
||||
<li><a href="._NeuralNet-bs020.html">21</a></li>
|
||||
<li><a href="._NeuralNet-bs021.html">22</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs013.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -261,7 +274,7 @@ variables are the input values \( x_n \).
|
||||
<li><a href="._NeuralNet-bs021.html">22</a></li>
|
||||
<li><a href="._NeuralNet-bs022.html">23</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
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|
||||
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|
||||
</ul>
|
||||
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|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -270,7 +283,7 @@ flexibility of a neural network.
|
||||
<li><a href="._NeuralNet-bs022.html">23</a></li>
|
||||
<li><a href="._NeuralNet-bs023.html">24</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
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|
||||
<li><a href="._NeuralNet-bs015.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
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|
||||
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|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
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|
||||
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|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -280,7 +293,7 @@ $$
|
||||
<li><a href="._NeuralNet-bs023.html">24</a></li>
|
||||
<li><a href="._NeuralNet-bs024.html">25</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs016.html">»</a></li>
|
||||
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|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -264,7 +277,7 @@ used as input to the activation functions. For each operation
|
||||
<li><a href="._NeuralNet-bs024.html">25</a></li>
|
||||
<li><a href="._NeuralNet-bs025.html">26</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs017.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -258,7 +271,7 @@ for a FFNN to fulfill the universal approximation theorem
|
||||
<li><a href="._NeuralNet-bs025.html">26</a></li>
|
||||
<li><a href="._NeuralNet-bs026.html">27</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs018.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -266,7 +279,7 @@ $$
|
||||
<li><a href="._NeuralNet-bs026.html">27</a></li>
|
||||
<li><a href="._NeuralNet-bs027.html">28</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs019.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -328,7 +341,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._NeuralNet-bs027.html">28</a></li>
|
||||
<li><a href="._NeuralNet-bs028.html">29</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
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|
||||
<li><a href="._NeuralNet-bs020.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
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|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -279,7 +292,7 @@ like logistic regression or linear regression and their modifications on the oth
|
||||
<li><a href="._NeuralNet-bs028.html">29</a></li>
|
||||
<li><a href="._NeuralNet-bs029.html">30</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs021.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -269,7 +282,7 @@ the potential of being universal approximators.
|
||||
<li><a href="._NeuralNet-bs029.html">30</a></li>
|
||||
<li><a href="._NeuralNet-bs030.html">31</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs022.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -275,7 +288,7 @@ classes.
|
||||
<li><a href="._NeuralNet-bs030.html">31</a></li>
|
||||
<li><a href="._NeuralNet-bs031.html">32</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs023.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -280,7 +293,7 @@ $$
|
||||
<li><a href="._NeuralNet-bs031.html">32</a></li>
|
||||
<li><a href="._NeuralNet-bs032.html">33</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs024.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -263,7 +276,7 @@ $$
|
||||
<li><a href="._NeuralNet-bs032.html">33</a></li>
|
||||
<li><a href="._NeuralNet-bs033.html">34</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs025.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -266,7 +279,7 @@ $$
|
||||
<li><a href="._NeuralNet-bs033.html">34</a></li>
|
||||
<li><a href="._NeuralNet-bs034.html">35</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs026.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -291,7 +304,7 @@ $$
|
||||
<li><a href="._NeuralNet-bs034.html">35</a></li>
|
||||
<li><a href="._NeuralNet-bs035.html">36</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs027.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
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||||
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||||
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||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
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|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
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|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -258,7 +271,7 @@ That is, the error \( \delta_j^L \) is exactly equal to the rate of change of th
|
||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -301,7 +314,7 @@ one \( L-1 \) in terms of the errors in the final output layer.
|
||||
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|
||||
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||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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||||
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||||
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||||
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||||
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|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
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|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
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|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
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|
||||
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||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -273,7 +286,7 @@ We are now ready to set up the algorithm for back propagation and learning the w
|
||||
<li><a href="._NeuralNet-bs037.html">38</a></li>
|
||||
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||||
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||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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||||
None,
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||||
'___sec47'),
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||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
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||||
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||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -317,7 +330,7 @@ Here it is convenient to use stochastic radient descent with mini-batches with a
|
||||
<li><a href="._NeuralNet-bs038.html">39</a></li>
|
||||
<li><a href="._NeuralNet-bs039.html">40</a></li>
|
||||
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|
||||
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||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -279,7 +292,7 @@ of our network.
|
||||
<li><a href="._NeuralNet-bs039.html">40</a></li>
|
||||
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|
||||
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||||
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@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
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|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
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|
||||
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<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -302,7 +315,7 @@ We leave it as an exercise in project 2 to derive these equations.
|
||||
<li><a href="._NeuralNet-bs040.html">41</a></li>
|
||||
<li><a href="._NeuralNet-bs041.html">42</a></li>
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@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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||||
None,
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||||
'___sec47'),
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||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
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<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -257,7 +270,7 @@ One can identify a set of key steps when using neural networks to solve supervis
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||||
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|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
end of tocinfo -->
|
||||
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||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -336,7 +349,7 @@ plt<span style="color: #666666">.</span>show()
|
||||
<li><a href="._NeuralNet-bs042.html">43</a></li>
|
||||
<li><a href="._NeuralNet-bs043.html">44</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
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|
||||
<li><a href="._NeuralNet-bs035.html">»</a></li>
|
||||
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|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -290,7 +303,7 @@ X_train, X_test, Y_train, Y_test <span style="color: #666666">=</span> train_tes
|
||||
<li><a href="._NeuralNet-bs043.html">44</a></li>
|
||||
<li><a href="._NeuralNet-bs044.html">45</a></li>
|
||||
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|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs036.html">»</a></li>
|
||||
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|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -287,7 +300,7 @@ which is inspired by probability theory (see logistic regression) and was most c
|
||||
<li><a href="._NeuralNet-bs044.html">45</a></li>
|
||||
<li><a href="._NeuralNet-bs045.html">46</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs037.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -286,7 +299,7 @@ weights to the output layer.
|
||||
<li><a href="._NeuralNet-bs045.html">46</a></li>
|
||||
<li><a href="._NeuralNet-bs046.html">47</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs038.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -277,7 +290,7 @@ output_bias <span style="color: #666666">=</span> np<span style="color: #666666"
|
||||
<li><a href="._NeuralNet-bs046.html">47</a></li>
|
||||
<li><a href="._NeuralNet-bs047.html">48</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs050.html">51</a></li>
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
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|
||||
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|
||||
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|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -268,7 +281,7 @@ $$ a_{j}^{o} = \frac{\exp{(z_j^{o})}}
|
||||
<li><a href="._NeuralNet-bs047.html">48</a></li>
|
||||
<li><a href="._NeuralNet-bs048.html">49</a></li>
|
||||
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|
||||
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|
||||
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|
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|
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|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
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||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
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<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -316,7 +329,7 @@ predictions <span style="color: #666666">=</span> predict(X_train)
|
||||
<li><a href="._NeuralNet-bs048.html">49</a></li>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
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|
||||
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|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
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|
||||
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|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
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|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -282,6 +295,8 @@ A full derivation is given in the appendix at the end.
|
||||
<li><a href="._NeuralNet-bs048.html">49</a></li>
|
||||
<li><a href="._NeuralNet-bs049.html">50</a></li>
|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
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|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
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|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
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|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
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||||
|
||||
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|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -276,6 +289,9 @@ This has two important benefits:
|
||||
<li><a href="._NeuralNet-bs048.html">49</a></li>
|
||||
<li><a href="._NeuralNet-bs049.html">50</a></li>
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||||
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|
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|
||||
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||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -271,6 +284,10 @@ calculate the gradient efficently.
|
||||
<li><a href="._NeuralNet-bs048.html">49</a></li>
|
||||
<li><a href="._NeuralNet-bs049.html">50</a></li>
|
||||
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|
||||
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -354,6 +367,11 @@ lmbd <span style="color: #666666">=</span> <span style="color: #666666">0.01</sp
|
||||
<li><a href="._NeuralNet-bs048.html">49</a></li>
|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
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|
||||
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|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
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|
||||
|
||||
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|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -256,6 +269,12 @@ Andrew Ng goes through some of these considerations in this <a href="https://you
|
||||
<li><a href="._NeuralNet-bs048.html">49</a></li>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
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|
||||
|
||||
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|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>And then with Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
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|
||||
@@ -348,6 +361,11 @@ being realizations of this object with different hyperparameters. An implementat
|
||||
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|
||||
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@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
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||||
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|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
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|
||||
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||||
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||||
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|
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|
||||
<!-- navigation toc: --> <li><a href="#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
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|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
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</ul>
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<h2 id="___sec49" class="anchor">And then with Tensorflow </h2>
|
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<h2 id="___sec49" class="anchor">Building neural networks in Tensorflow and Keras </h2>
|
||||
|
||||
<p>
|
||||
Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn
|
||||
and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
|
||||
and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.
|
||||
|
||||
<p>
|
||||
In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite
|
||||
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|
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs001.html#___sec0" style="font-size: 80%;"><b>Neural networks</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs002.html#___sec1" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs003.html#___sec2" style="font-size: 80%;"><b>Neural network types</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs004.html#___sec3" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs005.html#___sec4" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs006.html#___sec5" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs007.html#___sec6" style="font-size: 80%;"><b>Other types of networks</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs008.html#___sec7" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs009.html#___sec8" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs010.html#___sec9" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs011.html#___sec10" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs012.html#___sec11" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs013.html#___sec12" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs014.html#___sec13" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs015.html#___sec14" style="font-size: 80%;"> Matrix-vector notation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs016.html#___sec15" style="font-size: 80%;"> Matrix-vector notation and activation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs017.html#___sec16" style="font-size: 80%;"> Activation functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs018.html#___sec17" style="font-size: 80%;"> Activation functions, Logistic and Hyperbolic ones</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs019.html#___sec18" style="font-size: 80%;"> Relevance</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs020.html#___sec19" style="font-size: 80%;"><b>The multilayer perceptron (MLP)</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs021.html#___sec20" style="font-size: 80%;"><b>From one to many layers, the universal approximation theorem</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs022.html#___sec21" style="font-size: 80%;"><b>Deriving the back propagation code for a multilayer perceptron model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs023.html#___sec22" style="font-size: 80%;"><b>Definitions</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs024.html#___sec23" style="font-size: 80%;"><b>Derivatives and the chain rule</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs025.html#___sec24" style="font-size: 80%;"><b>Derivative of the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs026.html#___sec25" style="font-size: 80%;"><b>Bringing it together, first back propagation equation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs027.html#___sec26" style="font-size: 80%;"><b>Derivatives in terms of \( z_j^L \)</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs028.html#___sec27" style="font-size: 80%;"><b>Bringing it together</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs029.html#___sec28" style="font-size: 80%;"><b>Final back propagating equation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs030.html#___sec29" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs031.html#___sec30" style="font-size: 80%;"><b>Setting up a Multi-layer perceptron model for classification</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs032.html#___sec31" style="font-size: 80%;"><b>Defining the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs033.html#___sec32" style="font-size: 80%;"><b>Developing a code for doing neural networks with back propagation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs034.html#___sec33" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs035.html#___sec34" style="font-size: 80%;"><b>Train and test datasets</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs036.html#___sec35" style="font-size: 80%;"><b>Define model and architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs037.html#___sec36" style="font-size: 80%;"><b>Layers</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs038.html#___sec37" style="font-size: 80%;"><b>Weights and biases</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs039.html#___sec38" style="font-size: 80%;"><b>Feed-forward pass</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs040.html#___sec39" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs041.html#___sec40" style="font-size: 80%;"><b>Choose cost function and optimizer</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs042.html#___sec41" style="font-size: 80%;"><b>Optimizing the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs043.html#___sec42" style="font-size: 80%;"><b>Regularization</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs044.html#___sec43" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs045.html#___sec44" style="font-size: 80%;"><b>Improving performance</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs046.html#___sec45" style="font-size: 80%;"><b>Full object-oriented implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
<a name="part0051"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec50" class="anchor">Tensorflow </h2>
|
||||
|
||||
<p>
|
||||
Tensorflow is an open source library machine learning library
|
||||
developed by the Google Brain team for internal use. It was released
|
||||
under the Apache 2.0 open source license in November 9, 2015.
|
||||
|
||||
<p>
|
||||
Tensorflow is a computational framework that allows you to construct
|
||||
machine learning models at different levels of abstraction, from
|
||||
high-level, object-oriented APIs like Keras, down to the C++ kernels
|
||||
that Tensorflow is built upon. The higher levels of abstraction are
|
||||
simpler to use, but less flexible, and our choice of implementation
|
||||
should reflect the problems we are trying to solve.
|
||||
|
||||
<p>
|
||||
<a href="https://www.tensorflow.org/guide/graphs" target="_self">Tensorflow uses</a> so-called graphs to represent your computation
|
||||
in terms of the dependencies between individual operations, such that you first build a Tensorflow <em>graph</em>
|
||||
to represent your model, and then create a Tensorflow <em>session</em> to run the graph.
|
||||
|
||||
<p>
|
||||
In this guide we will analyze the same data as we did in our NumPy and
|
||||
scikit-learn tutorial, gathered from the MNIST database of images. We
|
||||
will give an introduction to the lower level Python Application
|
||||
Program Interfaces (APIs), and see how we use them to build our graph.
|
||||
Then we will build (effectively) the same graph in Keras, to see just
|
||||
how simple solving a machine learning problem can be.
|
||||
|
||||
<p>
|
||||
To install tensorflow on Unix/Linux systems, use pip as
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pip3 install tensorflow
|
||||
</pre></div>
|
||||
<p>
|
||||
and/or if you use <b>anaconda</b>, just write (or install from the graphical user interface)
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>conda install tensorflow
|
||||
</pre></div>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs001.html#___sec0" style="font-size: 80%;"><b>Neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs002.html#___sec1" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs003.html#___sec2" style="font-size: 80%;"><b>Neural network types</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs004.html#___sec3" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs005.html#___sec4" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs006.html#___sec5" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs007.html#___sec6" style="font-size: 80%;"><b>Other types of networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs008.html#___sec7" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs009.html#___sec8" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs010.html#___sec9" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs011.html#___sec10" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs012.html#___sec11" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs013.html#___sec12" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs014.html#___sec13" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs015.html#___sec14" style="font-size: 80%;"> Matrix-vector notation</a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs016.html#___sec15" style="font-size: 80%;"> Matrix-vector notation and activation</a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs017.html#___sec16" style="font-size: 80%;"> Activation functions</a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs018.html#___sec17" style="font-size: 80%;"> Activation functions, Logistic and Hyperbolic ones</a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs019.html#___sec18" style="font-size: 80%;"> Relevance</a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs020.html#___sec19" style="font-size: 80%;"><b>The multilayer perceptron (MLP)</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs021.html#___sec20" style="font-size: 80%;"><b>From one to many layers, the universal approximation theorem</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs022.html#___sec21" style="font-size: 80%;"><b>Deriving the back propagation code for a multilayer perceptron model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs023.html#___sec22" style="font-size: 80%;"><b>Definitions</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs024.html#___sec23" style="font-size: 80%;"><b>Derivatives and the chain rule</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs025.html#___sec24" style="font-size: 80%;"><b>Derivative of the cost function</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs026.html#___sec25" style="font-size: 80%;"><b>Bringing it together, first back propagation equation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs027.html#___sec26" style="font-size: 80%;"><b>Derivatives in terms of \( z_j^L \)</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs028.html#___sec27" style="font-size: 80%;"><b>Bringing it together</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs029.html#___sec28" style="font-size: 80%;"><b>Final back propagating equation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs030.html#___sec29" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs031.html#___sec30" style="font-size: 80%;"><b>Setting up a Multi-layer perceptron model for classification</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs032.html#___sec31" style="font-size: 80%;"><b>Defining the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs033.html#___sec32" style="font-size: 80%;"><b>Developing a code for doing neural networks with back propagation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs034.html#___sec33" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs035.html#___sec34" style="font-size: 80%;"><b>Train and test datasets</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs036.html#___sec35" style="font-size: 80%;"><b>Define model and architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs037.html#___sec36" style="font-size: 80%;"><b>Layers</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs038.html#___sec37" style="font-size: 80%;"><b>Weights and biases</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs039.html#___sec38" style="font-size: 80%;"><b>Feed-forward pass</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs040.html#___sec39" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs041.html#___sec40" style="font-size: 80%;"><b>Choose cost function and optimizer</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs042.html#___sec41" style="font-size: 80%;"><b>Optimizing the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs043.html#___sec42" style="font-size: 80%;"><b>Regularization</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs044.html#___sec43" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs045.html#___sec44" style="font-size: 80%;"><b>Improving performance</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs046.html#___sec45" style="font-size: 80%;"><b>Full object-oriented implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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||||
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||||
<a name="part0052"></a>
|
||||
<!-- !split -->
|
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|
||||
<h2 id="___sec51" class="anchor">Collect and pre-process data </h2>
|
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|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># import necessary packages</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> datasets
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># ensure the same random numbers appear every time</span>
|
||||
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">0</span>)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># display images in notebook</span>
|
||||
<span style="color: #666666">%</span>matplotlib inline
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'figure.figsize'</span>] <span style="color: #666666">=</span> (<span style="color: #666666">12</span>,<span style="color: #666666">12</span>)
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># download MNIST dataset</span>
|
||||
digits <span style="color: #666666">=</span> datasets<span style="color: #666666">.</span>load_digits()
|
||||
|
||||
<span style="color: #408080; font-style: italic"># define inputs and labels</span>
|
||||
inputs <span style="color: #666666">=</span> digits<span style="color: #666666">.</span>images
|
||||
labels <span style="color: #666666">=</span> digits<span style="color: #666666">.</span>target
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"inputs = (n_inputs, pixel_width, pixel_height) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(inputs<span style="color: #666666">.</span>shape))
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"labels = (n_inputs) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(labels<span style="color: #666666">.</span>shape))
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># flatten the image</span>
|
||||
<span style="color: #408080; font-style: italic"># the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64</span>
|
||||
n_inputs <span style="color: #666666">=</span> <span style="color: #008000">len</span>(inputs)
|
||||
inputs <span style="color: #666666">=</span> inputs<span style="color: #666666">.</span>reshape(n_inputs, <span style="color: #666666">-1</span>)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"X = (n_inputs, n_features) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(inputs<span style="color: #666666">.</span>shape))
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># choose some random images to display</span>
|
||||
indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(n_inputs)
|
||||
random_indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>choice(indices, size<span style="color: #666666">=5</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i, image <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(digits<span style="color: #666666">.</span>images[random_indices]):
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">1</span>, <span style="color: #666666">5</span>, i<span style="color: #666666">+1</span>)
|
||||
plt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">'off'</span>)
|
||||
plt<span style="color: #666666">.</span>imshow(image, cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>gray_r, interpolation<span style="color: #666666">=</span><span style="color: #BA2121">'nearest'</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Label: </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> digits<span style="color: #666666">.</span>target[random_indices[i]])
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.utils</span> <span style="color: #008000; font-weight: bold">import</span> to_categorical
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
|
||||
|
||||
<span style="color: #408080; font-style: italic"># one-hot representation of labels</span>
|
||||
labels <span style="color: #666666">=</span> to_categorical(labels)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># split into train and test data</span>
|
||||
train_size <span style="color: #666666">=</span> <span style="color: #666666">0.8</span>
|
||||
test_size <span style="color: #666666">=</span> <span style="color: #666666">1</span> <span style="color: #666666">-</span> train_size
|
||||
X_train, X_test, Y_train, Y_test <span style="color: #666666">=</span> train_test_split(inputs, labels, train_size<span style="color: #666666">=</span>train_size,
|
||||
test_size<span style="color: #666666">=</span>test_size)
|
||||
</pre></div>
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<!-- tocinfo
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{'highest level': 2,
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'sections': [('Neural networks', 2, None, '___sec0'),
|
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('Artificial neurons', 2, None, '___sec1'),
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('Neural network types', 2, None, '___sec2'),
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('Feed-forward neural networks', 2, None, '___sec3'),
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('Convolutional Neural Network', 2, None, '___sec4'),
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('Recurrent neural networks', 2, None, '___sec5'),
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|
||||
('Mathematical model', 2, None, '___sec10'),
|
||||
('Mathematical model', 2, None, '___sec11'),
|
||||
('Mathematical model', 2, None, '___sec12'),
|
||||
('Mathematical model', 2, None, '___sec13'),
|
||||
('Matrix-vector notation', 3, None, '___sec14'),
|
||||
('Matrix-vector notation and activation', 3, None, '___sec15'),
|
||||
('Activation functions', 3, None, '___sec16'),
|
||||
('Activation functions, Logistic and Hyperbolic ones',
|
||||
3,
|
||||
None,
|
||||
'___sec17'),
|
||||
('Relevance', 3, None, '___sec18'),
|
||||
('The multilayer perceptron (MLP)', 2, None, '___sec19'),
|
||||
('From one to many layers, the universal approximation theorem',
|
||||
2,
|
||||
None,
|
||||
'___sec20'),
|
||||
('Deriving the back propagation code for a multilayer perceptron '
|
||||
'model',
|
||||
2,
|
||||
None,
|
||||
'___sec21'),
|
||||
('Definitions', 2, None, '___sec22'),
|
||||
('Derivatives and the chain rule', 2, None, '___sec23'),
|
||||
('Derivative of the cost function', 2, None, '___sec24'),
|
||||
('Bringing it together, first back propagation equation',
|
||||
2,
|
||||
None,
|
||||
'___sec25'),
|
||||
('Derivatives in terms of $z_j^L$', 2, None, '___sec26'),
|
||||
('Bringing it together', 2, None, '___sec27'),
|
||||
('Final back propagating equation', 2, None, '___sec28'),
|
||||
('Setting up the Back propagation algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec29'),
|
||||
('Setting up a Multi-layer perceptron model for classification',
|
||||
2,
|
||||
None,
|
||||
'___sec30'),
|
||||
('Defining the cost function', 2, None, '___sec31'),
|
||||
('Developing a code for doing neural networks with back '
|
||||
'propagation',
|
||||
2,
|
||||
None,
|
||||
'___sec32'),
|
||||
('Collect and pre-process data', 2, None, '___sec33'),
|
||||
('Train and test datasets', 2, None, '___sec34'),
|
||||
('Define model and architecture', 2, None, '___sec35'),
|
||||
('Layers', 2, None, '___sec36'),
|
||||
('Weights and biases', 2, None, '___sec37'),
|
||||
('Feed-forward pass', 2, None, '___sec38'),
|
||||
('Matrix multiplication', 2, None, '___sec39'),
|
||||
('Choose cost function and optimizer', 2, None, '___sec40'),
|
||||
('Optimizing the cost function', 2, None, '___sec41'),
|
||||
('Regularization', 2, None, '___sec42'),
|
||||
('Matrix multiplication', 2, None, '___sec43'),
|
||||
('Improving performance', 2, None, '___sec44'),
|
||||
('Full object-oriented implementation', 2, None, '___sec45'),
|
||||
('Evaluate model performance on test data', 2, None, '___sec46'),
|
||||
('Adjust hyperparameters (if necessary, network architecture',
|
||||
2,
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
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<a class="navbar-brand" href="NeuralNet-bs.html">Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs001.html#___sec0" style="font-size: 80%;"><b>Neural networks</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs002.html#___sec1" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs003.html#___sec2" style="font-size: 80%;"><b>Neural network types</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs004.html#___sec3" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs005.html#___sec4" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs006.html#___sec5" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs007.html#___sec6" style="font-size: 80%;"><b>Other types of networks</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs008.html#___sec7" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs009.html#___sec8" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs010.html#___sec9" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs011.html#___sec10" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs012.html#___sec11" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs013.html#___sec12" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs014.html#___sec13" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs015.html#___sec14" style="font-size: 80%;"> Matrix-vector notation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs016.html#___sec15" style="font-size: 80%;"> Matrix-vector notation and activation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs017.html#___sec16" style="font-size: 80%;"> Activation functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs018.html#___sec17" style="font-size: 80%;"> Activation functions, Logistic and Hyperbolic ones</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs019.html#___sec18" style="font-size: 80%;"> Relevance</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs020.html#___sec19" style="font-size: 80%;"><b>The multilayer perceptron (MLP)</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs021.html#___sec20" style="font-size: 80%;"><b>From one to many layers, the universal approximation theorem</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs022.html#___sec21" style="font-size: 80%;"><b>Deriving the back propagation code for a multilayer perceptron model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs023.html#___sec22" style="font-size: 80%;"><b>Definitions</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs024.html#___sec23" style="font-size: 80%;"><b>Derivatives and the chain rule</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs025.html#___sec24" style="font-size: 80%;"><b>Derivative of the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs026.html#___sec25" style="font-size: 80%;"><b>Bringing it together, first back propagation equation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs027.html#___sec26" style="font-size: 80%;"><b>Derivatives in terms of \( z_j^L \)</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs028.html#___sec27" style="font-size: 80%;"><b>Bringing it together</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs029.html#___sec28" style="font-size: 80%;"><b>Final back propagating equation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs030.html#___sec29" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs031.html#___sec30" style="font-size: 80%;"><b>Setting up a Multi-layer perceptron model for classification</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs032.html#___sec31" style="font-size: 80%;"><b>Defining the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs033.html#___sec32" style="font-size: 80%;"><b>Developing a code for doing neural networks with back propagation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs034.html#___sec33" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs035.html#___sec34" style="font-size: 80%;"><b>Train and test datasets</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs036.html#___sec35" style="font-size: 80%;"><b>Define model and architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs037.html#___sec36" style="font-size: 80%;"><b>Layers</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs038.html#___sec37" style="font-size: 80%;"><b>Weights and biases</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs039.html#___sec38" style="font-size: 80%;"><b>Feed-forward pass</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs040.html#___sec39" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs041.html#___sec40" style="font-size: 80%;"><b>Choose cost function and optimizer</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs042.html#___sec41" style="font-size: 80%;"><b>Optimizing the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs043.html#___sec42" style="font-size: 80%;"><b>Regularization</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs044.html#___sec43" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs045.html#___sec44" style="font-size: 80%;"><b>Improving performance</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs046.html#___sec45" style="font-size: 80%;"><b>Full object-oriented implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
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|
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|
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<div class="container">
|
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|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
|
||||
<a name="part0053"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec52" class="anchor">Using TensorFlow backend </h2>
|
||||
|
||||
<ol>
|
||||
<li> Define model and architecture</li>
|
||||
<li> Choose cost function and optimizer</li>
|
||||
</ol>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">tensorflow</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">tf</span>
|
||||
|
||||
<span style="color: #008000; font-weight: bold">class</span> <span style="color: #0000FF; font-weight: bold">NeuralNetworkTensorflow</span>:
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">__init__</span>(
|
||||
<span style="color: #008000">self</span>,
|
||||
X_train,
|
||||
Y_train,
|
||||
X_test,
|
||||
Y_test,
|
||||
n_neurons_layer1<span style="color: #666666">=100</span>,
|
||||
n_neurons_layer2<span style="color: #666666">=50</span>,
|
||||
n_categories<span style="color: #666666">=2</span>,
|
||||
epochs<span style="color: #666666">=10</span>,
|
||||
batch_size<span style="color: #666666">=100</span>,
|
||||
eta<span style="color: #666666">=0.1</span>,
|
||||
lmbd<span style="color: #666666">=0.0</span>,
|
||||
):
|
||||
|
||||
<span style="color: #408080; font-style: italic"># keep track of number of steps</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>global_step <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>Variable(<span style="color: #666666">0</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>int32, trainable<span style="color: #666666">=</span><span style="color: #008000">False</span>, name<span style="color: #666666">=</span><span style="color: #BA2121">'global_step'</span>)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>X_train <span style="color: #666666">=</span> X_train
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>Y_train <span style="color: #666666">=</span> Y_train
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>X_test <span style="color: #666666">=</span> X_test
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>Y_test <span style="color: #666666">=</span> Y_test
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>n_inputs <span style="color: #666666">=</span> X_train<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>]
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>n_features <span style="color: #666666">=</span> X_train<span style="color: #666666">.</span>shape[<span style="color: #666666">1</span>]
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1 <span style="color: #666666">=</span> n_neurons_layer1
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2 <span style="color: #666666">=</span> n_neurons_layer2
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories <span style="color: #666666">=</span> n_categories
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>epochs <span style="color: #666666">=</span> epochs
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>batch_size <span style="color: #666666">=</span> batch_size
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>iterations <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>n_inputs <span style="color: #666666">//</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>batch_size
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>eta <span style="color: #666666">=</span> eta
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>lmbd <span style="color: #666666">=</span> lmbd
|
||||
|
||||
<span style="color: #408080; font-style: italic"># build network piece by piece</span>
|
||||
<span style="color: #408080; font-style: italic"># name scopes (with) are used to enforce creation of new variables</span>
|
||||
<span style="color: #408080; font-style: italic"># https://www.tensorflow.org/guide/variables</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>create_placeholders()
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>create_DNN()
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>create_loss()
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>create_optimiser()
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>create_accuracy()
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_placeholders</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #408080; font-style: italic"># placeholders are fine here, but "Datasets" are the preferred method</span>
|
||||
<span style="color: #408080; font-style: italic"># of streaming data into a model</span>
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'data'</span>):
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>X <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>placeholder(tf<span style="color: #666666">.</span>float32, shape<span style="color: #666666">=</span>(<span style="color: #008000">None</span>, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_features), name<span style="color: #666666">=</span><span style="color: #BA2121">'X_data'</span>)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>Y <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>placeholder(tf<span style="color: #666666">.</span>float32, shape<span style="color: #666666">=</span>(<span style="color: #008000">None</span>, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories), name<span style="color: #666666">=</span><span style="color: #BA2121">'Y_data'</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_DNN</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'DNN'</span>):
|
||||
<span style="color: #408080; font-style: italic"># the weights are stored to calculate regularization loss later</span>
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Fully connected layer 1</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc1 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>weight_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_features, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc1'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
b_fc1 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>bias_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc1'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
a_fc1 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>sigmoid(tf<span style="color: #666666">.</span>matmul(<span style="color: #008000">self</span><span style="color: #666666">.</span>X, <span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc1) <span style="color: #666666">+</span> b_fc1)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Fully connected layer 2</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc2 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>weight_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc2'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
b_fc2 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>bias_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc2'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
a_fc2 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>sigmoid(tf<span style="color: #666666">.</span>matmul(a_fc1, <span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc2) <span style="color: #666666">+</span> b_fc2)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Output layer</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>W_out <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>weight_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories], name<span style="color: #666666">=</span><span style="color: #BA2121">'out'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
b_out <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>bias_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories], name<span style="color: #666666">=</span><span style="color: #BA2121">'out'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>z_out <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>matmul(a_fc2, <span style="color: #008000">self</span><span style="color: #666666">.</span>W_out) <span style="color: #666666">+</span> b_out
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_loss</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'loss'</span>):
|
||||
softmax_loss <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>reduce_mean(tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>softmax_cross_entropy_with_logits_v2(labels<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>Y, logits<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>z_out))
|
||||
|
||||
regularizer_loss_fc1 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>l2_loss(<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc1)
|
||||
regularizer_loss_fc2 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>l2_loss(<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc2)
|
||||
regularizer_loss_out <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>l2_loss(<span style="color: #008000">self</span><span style="color: #666666">.</span>W_out)
|
||||
regularizer_loss <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>lmbd<span style="color: #666666">*</span>(regularizer_loss_fc1 <span style="color: #666666">+</span> regularizer_loss_fc2 <span style="color: #666666">+</span> regularizer_loss_out)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>loss <span style="color: #666666">=</span> softmax_loss <span style="color: #666666">+</span> regularizer_loss
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_accuracy</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'accuracy'</span>):
|
||||
probabilities <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>softmax(<span style="color: #008000">self</span><span style="color: #666666">.</span>z_out)
|
||||
predictions <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>argmax(probabilities, axis<span style="color: #666666">=1</span>)
|
||||
labels <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>argmax(<span style="color: #008000">self</span><span style="color: #666666">.</span>Y, axis<span style="color: #666666">=1</span>)
|
||||
|
||||
correct_predictions <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>equal(predictions, labels)
|
||||
correct_predictions <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>cast(correct_predictions, tf<span style="color: #666666">.</span>float32)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>accuracy <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>reduce_mean(correct_predictions)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_optimiser</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'optimizer'</span>):
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>optimizer <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>train<span style="color: #666666">.</span>GradientDescentOptimizer(learning_rate<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>eta)<span style="color: #666666">.</span>minimize(<span style="color: #008000">self</span><span style="color: #666666">.</span>loss, global_step<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>global_step)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">weight_variable</span>(<span style="color: #008000">self</span>, shape, name<span style="color: #666666">=</span><span style="color: #BA2121">''</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32):
|
||||
initial <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>truncated_normal(shape, stddev<span style="color: #666666">=0.1</span>)
|
||||
<span style="color: #008000; font-weight: bold">return</span> tf<span style="color: #666666">.</span>Variable(initial, name<span style="color: #666666">=</span>name, dtype<span style="color: #666666">=</span>dtype)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">bias_variable</span>(<span style="color: #008000">self</span>, shape, name<span style="color: #666666">=</span><span style="color: #BA2121">''</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32):
|
||||
initial <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>constant(<span style="color: #666666">0.1</span>, shape<span style="color: #666666">=</span>shape)
|
||||
<span style="color: #008000; font-weight: bold">return</span> tf<span style="color: #666666">.</span>Variable(initial, name<span style="color: #666666">=</span>name, dtype<span style="color: #666666">=</span>dtype)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">fit</span>(<span style="color: #008000">self</span>):
|
||||
data_indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #008000">self</span><span style="color: #666666">.</span>n_inputs)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>Session() <span style="color: #008000; font-weight: bold">as</span> sess:
|
||||
sess<span style="color: #666666">.</span>run(tf<span style="color: #666666">.</span>global_variables_initializer())
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">self</span><span style="color: #666666">.</span>epochs):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">self</span><span style="color: #666666">.</span>iterations):
|
||||
chosen_datapoints <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>choice(data_indices, size<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>batch_size, replace<span style="color: #666666">=</span><span style="color: #008000">False</span>)
|
||||
batch_X, batch_Y <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>X_train[chosen_datapoints], <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_train[chosen_datapoints]
|
||||
|
||||
sess<span style="color: #666666">.</span>run([DNN<span style="color: #666666">.</span>loss, DNN<span style="color: #666666">.</span>optimizer],
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: batch_X,
|
||||
DNN<span style="color: #666666">.</span>Y: batch_Y})
|
||||
accuracy <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run(DNN<span style="color: #666666">.</span>accuracy,
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: batch_X,
|
||||
DNN<span style="color: #666666">.</span>Y: batch_Y})
|
||||
step <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run(DNN<span style="color: #666666">.</span>global_step)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>train_loss, <span style="color: #008000">self</span><span style="color: #666666">.</span>train_accuracy <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run([DNN<span style="color: #666666">.</span>loss, DNN<span style="color: #666666">.</span>accuracy],
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: <span style="color: #008000">self</span><span style="color: #666666">.</span>X_train,
|
||||
DNN<span style="color: #666666">.</span>Y: <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_train})
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>test_loss, <span style="color: #008000">self</span><span style="color: #666666">.</span>test_accuracy <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run([DNN<span style="color: #666666">.</span>loss, DNN<span style="color: #666666">.</span>accuracy],
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: <span style="color: #008000">self</span><span style="color: #666666">.</span>X_test,
|
||||
DNN<span style="color: #666666">.</span>Y: <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_test})
|
||||
</pre></div>
|
||||
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|
||||
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||||
<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Neural networks', 2, None, '___sec0'),
|
||||
('Artificial neurons', 2, None, '___sec1'),
|
||||
('Neural network types', 2, None, '___sec2'),
|
||||
('Feed-forward neural networks', 2, None, '___sec3'),
|
||||
('Convolutional Neural Network', 2, None, '___sec4'),
|
||||
('Recurrent neural networks', 2, None, '___sec5'),
|
||||
('Other types of networks', 2, None, '___sec6'),
|
||||
('Multilayer perceptrons', 2, None, '___sec7'),
|
||||
('Why multilayer perceptrons?', 2, None, '___sec8'),
|
||||
('Mathematical model', 2, None, '___sec9'),
|
||||
('Mathematical model', 2, None, '___sec10'),
|
||||
('Mathematical model', 2, None, '___sec11'),
|
||||
('Mathematical model', 2, None, '___sec12'),
|
||||
('Mathematical model', 2, None, '___sec13'),
|
||||
('Matrix-vector notation', 3, None, '___sec14'),
|
||||
('Matrix-vector notation and activation', 3, None, '___sec15'),
|
||||
('Activation functions', 3, None, '___sec16'),
|
||||
('Activation functions, Logistic and Hyperbolic ones',
|
||||
3,
|
||||
None,
|
||||
'___sec17'),
|
||||
('Relevance', 3, None, '___sec18'),
|
||||
('The multilayer perceptron (MLP)', 2, None, '___sec19'),
|
||||
('From one to many layers, the universal approximation theorem',
|
||||
2,
|
||||
None,
|
||||
'___sec20'),
|
||||
('Deriving the back propagation code for a multilayer perceptron '
|
||||
'model',
|
||||
2,
|
||||
None,
|
||||
'___sec21'),
|
||||
('Definitions', 2, None, '___sec22'),
|
||||
('Derivatives and the chain rule', 2, None, '___sec23'),
|
||||
('Derivative of the cost function', 2, None, '___sec24'),
|
||||
('Bringing it together, first back propagation equation',
|
||||
2,
|
||||
None,
|
||||
'___sec25'),
|
||||
('Derivatives in terms of $z_j^L$', 2, None, '___sec26'),
|
||||
('Bringing it together', 2, None, '___sec27'),
|
||||
('Final back propagating equation', 2, None, '___sec28'),
|
||||
('Setting up the Back propagation algorithm',
|
||||
2,
|
||||
None,
|
||||
'___sec29'),
|
||||
('Setting up a Multi-layer perceptron model for classification',
|
||||
2,
|
||||
None,
|
||||
'___sec30'),
|
||||
('Defining the cost function', 2, None, '___sec31'),
|
||||
('Developing a code for doing neural networks with back '
|
||||
'propagation',
|
||||
2,
|
||||
None,
|
||||
'___sec32'),
|
||||
('Collect and pre-process data', 2, None, '___sec33'),
|
||||
('Train and test datasets', 2, None, '___sec34'),
|
||||
('Define model and architecture', 2, None, '___sec35'),
|
||||
('Layers', 2, None, '___sec36'),
|
||||
('Weights and biases', 2, None, '___sec37'),
|
||||
('Feed-forward pass', 2, None, '___sec38'),
|
||||
('Matrix multiplication', 2, None, '___sec39'),
|
||||
('Choose cost function and optimizer', 2, None, '___sec40'),
|
||||
('Optimizing the cost function', 2, None, '___sec41'),
|
||||
('Regularization', 2, None, '___sec42'),
|
||||
('Matrix multiplication', 2, None, '___sec43'),
|
||||
('Improving performance', 2, None, '___sec44'),
|
||||
('Full object-oriented implementation', 2, None, '___sec45'),
|
||||
('Evaluate model performance on test data', 2, None, '___sec46'),
|
||||
('Adjust hyperparameters (if necessary, network architecture',
|
||||
2,
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
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||||
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<a class="navbar-brand" href="NeuralNet-bs.html">Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs001.html#___sec0" style="font-size: 80%;"><b>Neural networks</b></a></li>
|
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs002.html#___sec1" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs003.html#___sec2" style="font-size: 80%;"><b>Neural network types</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs004.html#___sec3" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs005.html#___sec4" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs006.html#___sec5" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs007.html#___sec6" style="font-size: 80%;"><b>Other types of networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs008.html#___sec7" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs009.html#___sec8" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs010.html#___sec9" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs011.html#___sec10" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs012.html#___sec11" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs013.html#___sec12" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs014.html#___sec13" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs015.html#___sec14" style="font-size: 80%;"> Matrix-vector notation</a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs016.html#___sec15" style="font-size: 80%;"> Matrix-vector notation and activation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs017.html#___sec16" style="font-size: 80%;"> Activation functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs018.html#___sec17" style="font-size: 80%;"> Activation functions, Logistic and Hyperbolic ones</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs019.html#___sec18" style="font-size: 80%;"> Relevance</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs020.html#___sec19" style="font-size: 80%;"><b>The multilayer perceptron (MLP)</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs021.html#___sec20" style="font-size: 80%;"><b>From one to many layers, the universal approximation theorem</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs022.html#___sec21" style="font-size: 80%;"><b>Deriving the back propagation code for a multilayer perceptron model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs023.html#___sec22" style="font-size: 80%;"><b>Definitions</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs024.html#___sec23" style="font-size: 80%;"><b>Derivatives and the chain rule</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs025.html#___sec24" style="font-size: 80%;"><b>Derivative of the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs026.html#___sec25" style="font-size: 80%;"><b>Bringing it together, first back propagation equation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs027.html#___sec26" style="font-size: 80%;"><b>Derivatives in terms of \( z_j^L \)</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs028.html#___sec27" style="font-size: 80%;"><b>Bringing it together</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs029.html#___sec28" style="font-size: 80%;"><b>Final back propagating equation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs030.html#___sec29" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs031.html#___sec30" style="font-size: 80%;"><b>Setting up a Multi-layer perceptron model for classification</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs032.html#___sec31" style="font-size: 80%;"><b>Defining the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs033.html#___sec32" style="font-size: 80%;"><b>Developing a code for doing neural networks with back propagation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs034.html#___sec33" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs035.html#___sec34" style="font-size: 80%;"><b>Train and test datasets</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs036.html#___sec35" style="font-size: 80%;"><b>Define model and architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs037.html#___sec36" style="font-size: 80%;"><b>Layers</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs038.html#___sec37" style="font-size: 80%;"><b>Weights and biases</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs039.html#___sec38" style="font-size: 80%;"><b>Feed-forward pass</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs040.html#___sec39" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs041.html#___sec40" style="font-size: 80%;"><b>Choose cost function and optimizer</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs042.html#___sec41" style="font-size: 80%;"><b>Optimizing the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs043.html#___sec42" style="font-size: 80%;"><b>Regularization</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs044.html#___sec43" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs045.html#___sec44" style="font-size: 80%;"><b>Improving performance</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs046.html#___sec45" style="font-size: 80%;"><b>Full object-oriented implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
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|
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|
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<div class="container">
|
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|
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
|
||||
<a name="part0054"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec53" class="anchor">Optimizing and using gradient descent </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>epochs <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
batch_size <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
n_neurons_layer1 <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
n_neurons_layer2 <span style="color: #666666">=</span> <span style="color: #666666">50</span>
|
||||
n_categories <span style="color: #666666">=</span> <span style="color: #666666">10</span>
|
||||
|
||||
eta_vals <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-5</span>, <span style="color: #666666">1</span>, <span style="color: #666666">7</span>)
|
||||
lmbd_vals <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-5</span>, <span style="color: #666666">1</span>, <span style="color: #666666">7</span>)
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>DNN_tf <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)), dtype<span style="color: #666666">=</span><span style="color: #008000">object</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i, eta <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(eta_vals):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j, lmbd <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(lmbd_vals):
|
||||
DNN <span style="color: #666666">=</span> NeuralNetworkTensorflow(X_train, Y_train, X_test, Y_test,
|
||||
n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
epochs<span style="color: #666666">=</span>epochs, batch_size<span style="color: #666666">=</span>batch_size, eta<span style="color: #666666">=</span>eta, lmbd<span style="color: #666666">=</span>lmbd)
|
||||
DNN<span style="color: #666666">.</span>fit()
|
||||
|
||||
DNN_tf[i][j] <span style="color: #666666">=</span> DNN
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Learning rate = "</span>, eta)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Test accuracy: </span><span style="color: #BB6688; font-weight: bold">%.3f</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> DNN<span style="color: #666666">.</span>test_accuracy)
|
||||
<span style="color: #008000; font-weight: bold">print</span>()
|
||||
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># optional</span>
|
||||
<span style="color: #408080; font-style: italic"># visual representation of grid search</span>
|
||||
<span style="color: #408080; font-style: italic"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">seaborn</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sns</span>
|
||||
|
||||
sns<span style="color: #666666">.</span>set()
|
||||
|
||||
train_accuracy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)))
|
||||
test_accuracy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(eta_vals)):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(lmbd_vals)):
|
||||
DNN <span style="color: #666666">=</span> DNN_tf[i][j]
|
||||
|
||||
train_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>train_accuracy
|
||||
test_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>test_accuracy
|
||||
|
||||
|
||||
fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(figsize <span style="color: #666666">=</span> (<span style="color: #666666">10</span>, <span style="color: #666666">10</span>))
|
||||
sns<span style="color: #666666">.</span>heatmap(train_accuracy, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>, ax<span style="color: #666666">=</span>ax, cmap<span style="color: #666666">=</span><span style="color: #BA2121">"viridis"</span>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Training Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(figsize <span style="color: #666666">=</span> (<span style="color: #666666">10</span>, <span style="color: #666666">10</span>))
|
||||
sns<span style="color: #666666">.</span>heatmap(test_accuracy, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>, ax<span style="color: #666666">=</span>ax, cmap<span style="color: #666666">=</span><span style="color: #BA2121">"viridis"</span>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Test Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># optional</span>
|
||||
<span style="color: #408080; font-style: italic"># we can use log files to visualize our graph in Tensorboard</span>
|
||||
writer <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>summary<span style="color: #666666">.</span>FileWriter(<span style="color: #BA2121">'logs/'</span>)
|
||||
writer<span style="color: #666666">.</span>add_graph(tf<span style="color: #666666">.</span>get_default_graph())
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
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<ul class="dropdown-menu">
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs001.html#___sec0" style="font-size: 80%;"><b>Neural networks</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs002.html#___sec1" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs003.html#___sec2" style="font-size: 80%;"><b>Neural network types</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs004.html#___sec3" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs005.html#___sec4" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs006.html#___sec5" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs007.html#___sec6" style="font-size: 80%;"><b>Other types of networks</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs008.html#___sec7" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs009.html#___sec8" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs010.html#___sec9" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs011.html#___sec10" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs012.html#___sec11" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs013.html#___sec12" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs014.html#___sec13" style="font-size: 80%;"><b>Mathematical model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs015.html#___sec14" style="font-size: 80%;"> Matrix-vector notation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs016.html#___sec15" style="font-size: 80%;"> Matrix-vector notation and activation</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs017.html#___sec16" style="font-size: 80%;"> Activation functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs018.html#___sec17" style="font-size: 80%;"> Activation functions, Logistic and Hyperbolic ones</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs019.html#___sec18" style="font-size: 80%;"> Relevance</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs020.html#___sec19" style="font-size: 80%;"><b>The multilayer perceptron (MLP)</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs021.html#___sec20" style="font-size: 80%;"><b>From one to many layers, the universal approximation theorem</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs022.html#___sec21" style="font-size: 80%;"><b>Deriving the back propagation code for a multilayer perceptron model</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs023.html#___sec22" style="font-size: 80%;"><b>Definitions</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs024.html#___sec23" style="font-size: 80%;"><b>Derivatives and the chain rule</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs025.html#___sec24" style="font-size: 80%;"><b>Derivative of the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs026.html#___sec25" style="font-size: 80%;"><b>Bringing it together, first back propagation equation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs027.html#___sec26" style="font-size: 80%;"><b>Derivatives in terms of \( z_j^L \)</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs028.html#___sec27" style="font-size: 80%;"><b>Bringing it together</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs029.html#___sec28" style="font-size: 80%;"><b>Final back propagating equation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs030.html#___sec29" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs031.html#___sec30" style="font-size: 80%;"><b>Setting up a Multi-layer perceptron model for classification</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs032.html#___sec31" style="font-size: 80%;"><b>Defining the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs033.html#___sec32" style="font-size: 80%;"><b>Developing a code for doing neural networks with back propagation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs034.html#___sec33" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs035.html#___sec34" style="font-size: 80%;"><b>Train and test datasets</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs036.html#___sec35" style="font-size: 80%;"><b>Define model and architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs037.html#___sec36" style="font-size: 80%;"><b>Layers</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs038.html#___sec37" style="font-size: 80%;"><b>Weights and biases</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs039.html#___sec38" style="font-size: 80%;"><b>Feed-forward pass</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs040.html#___sec39" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs041.html#___sec40" style="font-size: 80%;"><b>Choose cost function and optimizer</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs042.html#___sec41" style="font-size: 80%;"><b>Optimizing the cost function</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs043.html#___sec42" style="font-size: 80%;"><b>Regularization</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs044.html#___sec43" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs045.html#___sec44" style="font-size: 80%;"><b>Improving performance</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs046.html#___sec45" style="font-size: 80%;"><b>Full object-oriented implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
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||||
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|
||||
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|
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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||||
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||||
<a name="part0055"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec54" class="anchor">Using Keras </h2>
|
||||
|
||||
<p>
|
||||
Keras is a high level <a href="https://en.wikipedia.org/wiki/Application_programming_interface" target="_self">neural network</a>
|
||||
that supports Tensorflow, CTNK and Theano as backends.
|
||||
If you have Tensorflow installed Keras is available through the <em>tf.keras</em> module.
|
||||
If you have Anaconda installed you may run the following command
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>conda install keras
|
||||
</pre></div>
|
||||
<p>
|
||||
Alternatively, if you have Tensorflow or one of the other supported backends install you may use the pip package manager:
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pip3 install keras
|
||||
</pre></div>
|
||||
<p>
|
||||
or look up the <a href="https://keras.io/" target="_self">instructions here</a>.
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.models</span> <span style="color: #008000; font-weight: bold">import</span> Sequential
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.layers</span> <span style="color: #008000; font-weight: bold">import</span> Dense
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.regularizers</span> <span style="color: #008000; font-weight: bold">import</span> l2
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.optimizers</span> <span style="color: #008000; font-weight: bold">import</span> SGD
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_neural_network_keras</span>(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
|
||||
model <span style="color: #666666">=</span> Sequential()
|
||||
model<span style="color: #666666">.</span>add(Dense(n_neurons_layer1, activation<span style="color: #666666">=</span><span style="color: #BA2121">'sigmoid'</span>, kernel_regularizer<span style="color: #666666">=</span>l2(lmbd)))
|
||||
model<span style="color: #666666">.</span>add(Dense(n_neurons_layer2, activation<span style="color: #666666">=</span><span style="color: #BA2121">'sigmoid'</span>, kernel_regularizer<span style="color: #666666">=</span>l2(lmbd)))
|
||||
model<span style="color: #666666">.</span>add(Dense(n_categories, activation<span style="color: #666666">=</span><span style="color: #BA2121">'softmax'</span>))
|
||||
|
||||
sgd <span style="color: #666666">=</span> SGD(lr<span style="color: #666666">=</span>eta)
|
||||
model<span style="color: #666666">.</span>compile(loss<span style="color: #666666">=</span><span style="color: #BA2121">'categorical_crossentropy'</span>, optimizer<span style="color: #666666">=</span>sgd, metrics<span style="color: #666666">=</span>[<span style="color: #BA2121">'accuracy'</span>])
|
||||
|
||||
<span style="color: #008000; font-weight: bold">return</span> model
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>DNN_keras <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)), dtype<span style="color: #666666">=</span><span style="color: #008000">object</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i, eta <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(eta_vals):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j, lmbd <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(lmbd_vals):
|
||||
DNN <span style="color: #666666">=</span> create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
eta<span style="color: #666666">=</span>eta, lmbd<span style="color: #666666">=</span>lmbd)
|
||||
DNN<span style="color: #666666">.</span>fit(X_train, Y_train, epochs<span style="color: #666666">=</span>epochs, batch_size<span style="color: #666666">=</span>batch_size, verbose<span style="color: #666666">=0</span>)
|
||||
scores <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>evaluate(X_test, Y_test)
|
||||
|
||||
DNN_keras[i][j] <span style="color: #666666">=</span> DNN
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Learning rate = "</span>, eta)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Test accuracy: </span><span style="color: #BB6688; font-weight: bold">%.3f</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> scores[<span style="color: #666666">1</span>])
|
||||
<span style="color: #008000; font-weight: bold">print</span>()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># optional</span>
|
||||
<span style="color: #408080; font-style: italic"># visual representation of grid search</span>
|
||||
<span style="color: #408080; font-style: italic"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">seaborn</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sns</span>
|
||||
|
||||
sns<span style="color: #666666">.</span>set()
|
||||
|
||||
train_accuracy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)))
|
||||
test_accuracy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(eta_vals)):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(lmbd_vals)):
|
||||
DNN <span style="color: #666666">=</span> DNN_keras[i][j]
|
||||
|
||||
train_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>evaluate(X_train, Y_train)[<span style="color: #666666">1</span>]
|
||||
test_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>evaluate(X_test, Y_test)[<span style="color: #666666">1</span>]
|
||||
|
||||
|
||||
fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(figsize <span style="color: #666666">=</span> (<span style="color: #666666">10</span>, <span style="color: #666666">10</span>))
|
||||
sns<span style="color: #666666">.</span>heatmap(train_accuracy, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>, ax<span style="color: #666666">=</span>ax, cmap<span style="color: #666666">=</span><span style="color: #BA2121">"viridis"</span>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Training Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(figsize <span style="color: #666666">=</span> (<span style="color: #666666">10</span>, <span style="color: #666666">10</span>))
|
||||
sns<span style="color: #666666">.</span>heatmap(test_accuracy, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>, ax<span style="color: #666666">=</span>ax, cmap<span style="color: #666666">=</span><span style="color: #BA2121">"viridis"</span>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Test Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
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|
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||||
|
||||
@@ -115,7 +115,15 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -202,7 +210,12 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -261,7 +274,7 @@ MathJax.Hub.Config({
|
||||
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|
||||
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|
||||
<!-- ------------------- end of main content --------------- -->
|
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|
||||
@@ -2334,7 +2334,456 @@ plt.show()
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec49">And then with Tensorflow </h2>
|
||||
<h2 id="___sec49">Building neural networks in Tensorflow and Keras </h2>
|
||||
|
||||
<p>
|
||||
Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn
|
||||
and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
|
||||
and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.
|
||||
|
||||
<p>
|
||||
In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite
|
||||
clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or
|
||||
NumPy arrays.
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec50">Tensorflow </h2>
|
||||
|
||||
<p>
|
||||
Tensorflow is an open source library machine learning library
|
||||
developed by the Google Brain team for internal use. It was released
|
||||
under the Apache 2.0 open source license in November 9, 2015.
|
||||
|
||||
<p>
|
||||
Tensorflow is a computational framework that allows you to construct
|
||||
machine learning models at different levels of abstraction, from
|
||||
high-level, object-oriented APIs like Keras, down to the C++ kernels
|
||||
that Tensorflow is built upon. The higher levels of abstraction are
|
||||
simpler to use, but less flexible, and our choice of implementation
|
||||
should reflect the problems we are trying to solve.
|
||||
|
||||
<p>
|
||||
<a href="https://www.tensorflow.org/guide/graphs" target="_blank">Tensorflow uses</a> so-called graphs to represent your computation
|
||||
in terms of the dependencies between individual operations, such that you first build a Tensorflow <em>graph</em>
|
||||
to represent your model, and then create a Tensorflow <em>session</em> to run the graph.
|
||||
|
||||
<p>
|
||||
In this guide we will analyze the same data as we did in our NumPy and
|
||||
scikit-learn tutorial, gathered from the MNIST database of images. We
|
||||
will give an introduction to the lower level Python Application
|
||||
Program Interfaces (APIs), and see how we use them to build our graph.
|
||||
Then we will build (effectively) the same graph in Keras, to see just
|
||||
how simple solving a machine learning problem can be.
|
||||
|
||||
<p>
|
||||
To install tensorflow on Unix/Linux systems, use pip as
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>pip3 install tensorflow
|
||||
</pre></div>
|
||||
<p>
|
||||
and/or if you use <b>anaconda</b>, just write (or install from the graphical user interface)
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>conda install tensorflow
|
||||
</pre></div>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec51">Collect and pre-process data </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># import necessary packages</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn</span> <span style="color: #8B008B; font-weight: bold">import</span> datasets
|
||||
|
||||
|
||||
<span style="color: #228B22"># ensure the same random numbers appear every time</span>
|
||||
np.random.seed(<span style="color: #B452CD">0</span>)
|
||||
|
||||
<span style="color: #228B22"># display images in notebook</span>
|
||||
%matplotlib inline
|
||||
plt.rcParams[<span style="color: #CD5555">'figure.figsize'</span>] = (<span style="color: #B452CD">12</span>,<span style="color: #B452CD">12</span>)
|
||||
|
||||
|
||||
<span style="color: #228B22"># download MNIST dataset</span>
|
||||
digits = datasets.load_digits()
|
||||
|
||||
<span style="color: #228B22"># define inputs and labels</span>
|
||||
inputs = digits.images
|
||||
labels = digits.target
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"inputs = (n_inputs, pixel_width, pixel_height) = "</span> + <span style="color: #658b00">str</span>(inputs.shape))
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"labels = (n_inputs) = "</span> + <span style="color: #658b00">str</span>(labels.shape))
|
||||
|
||||
|
||||
<span style="color: #228B22"># flatten the image</span>
|
||||
<span style="color: #228B22"># the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64</span>
|
||||
n_inputs = <span style="color: #658b00">len</span>(inputs)
|
||||
inputs = inputs.reshape(n_inputs, -<span style="color: #B452CD">1</span>)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"X = (n_inputs, n_features) = "</span> + <span style="color: #658b00">str</span>(inputs.shape))
|
||||
|
||||
|
||||
<span style="color: #228B22"># choose some random images to display</span>
|
||||
indices = np.arange(n_inputs)
|
||||
random_indices = np.random.choice(indices, size=<span style="color: #B452CD">5</span>)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i, image <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(digits.images[random_indices]):
|
||||
plt.subplot(<span style="color: #B452CD">1</span>, <span style="color: #B452CD">5</span>, i+<span style="color: #B452CD">1</span>)
|
||||
plt.axis(<span style="color: #CD5555">'off'</span>)
|
||||
plt.imshow(image, cmap=plt.cm.gray_r, interpolation=<span style="color: #CD5555">'nearest'</span>)
|
||||
plt.title(<span style="color: #CD5555">"Label: %d"</span> % digits.target[random_indices[i]])
|
||||
plt.show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.utils</span> <span style="color: #8B008B; font-weight: bold">import</span> to_categorical
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> train_test_split
|
||||
|
||||
<span style="color: #228B22"># one-hot representation of labels</span>
|
||||
labels = to_categorical(labels)
|
||||
|
||||
<span style="color: #228B22"># split into train and test data</span>
|
||||
train_size = <span style="color: #B452CD">0.8</span>
|
||||
test_size = <span style="color: #B452CD">1</span> - train_size
|
||||
X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
|
||||
test_size=test_size)
|
||||
</pre></div>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec52">Using TensorFlow backend </h2>
|
||||
|
||||
<ol>
|
||||
<p><li> Define model and architecture</li>
|
||||
<p><li> Choose cost function and optimizer</li>
|
||||
</ol>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">tensorflow</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">tf</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">class</span> <span style="color: #008b45; font-weight: bold">NeuralNetworkTensorflow</span>:
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">__init__</span>(
|
||||
<span style="color: #658b00">self</span>,
|
||||
X_train,
|
||||
Y_train,
|
||||
X_test,
|
||||
Y_test,
|
||||
n_neurons_layer1=<span style="color: #B452CD">100</span>,
|
||||
n_neurons_layer2=<span style="color: #B452CD">50</span>,
|
||||
n_categories=<span style="color: #B452CD">2</span>,
|
||||
epochs=<span style="color: #B452CD">10</span>,
|
||||
batch_size=<span style="color: #B452CD">100</span>,
|
||||
eta=<span style="color: #B452CD">0.1</span>,
|
||||
lmbd=<span style="color: #B452CD">0.0</span>,
|
||||
):
|
||||
|
||||
<span style="color: #228B22"># keep track of number of steps</span>
|
||||
<span style="color: #658b00">self</span>.global_step = tf.Variable(<span style="color: #B452CD">0</span>, dtype=tf.int32, trainable=<span style="color: #658b00">False</span>, name=<span style="color: #CD5555">'global_step'</span>)
|
||||
|
||||
<span style="color: #658b00">self</span>.X_train = X_train
|
||||
<span style="color: #658b00">self</span>.Y_train = Y_train
|
||||
<span style="color: #658b00">self</span>.X_test = X_test
|
||||
<span style="color: #658b00">self</span>.Y_test = Y_test
|
||||
|
||||
<span style="color: #658b00">self</span>.n_inputs = X_train.shape[<span style="color: #B452CD">0</span>]
|
||||
<span style="color: #658b00">self</span>.n_features = X_train.shape[<span style="color: #B452CD">1</span>]
|
||||
<span style="color: #658b00">self</span>.n_neurons_layer1 = n_neurons_layer1
|
||||
<span style="color: #658b00">self</span>.n_neurons_layer2 = n_neurons_layer2
|
||||
<span style="color: #658b00">self</span>.n_categories = n_categories
|
||||
|
||||
<span style="color: #658b00">self</span>.epochs = epochs
|
||||
<span style="color: #658b00">self</span>.batch_size = batch_size
|
||||
<span style="color: #658b00">self</span>.iterations = <span style="color: #658b00">self</span>.n_inputs // <span style="color: #658b00">self</span>.batch_size
|
||||
<span style="color: #658b00">self</span>.eta = eta
|
||||
<span style="color: #658b00">self</span>.lmbd = lmbd
|
||||
|
||||
<span style="color: #228B22"># build network piece by piece</span>
|
||||
<span style="color: #228B22"># name scopes (with) are used to enforce creation of new variables</span>
|
||||
<span style="color: #228B22"># https://www.tensorflow.org/guide/variables</span>
|
||||
<span style="color: #658b00">self</span>.create_placeholders()
|
||||
<span style="color: #658b00">self</span>.create_DNN()
|
||||
<span style="color: #658b00">self</span>.create_loss()
|
||||
<span style="color: #658b00">self</span>.create_optimiser()
|
||||
<span style="color: #658b00">self</span>.create_accuracy()
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_placeholders</span>(<span style="color: #658b00">self</span>):
|
||||
<span style="color: #228B22"># placeholders are fine here, but "Datasets" are the preferred method</span>
|
||||
<span style="color: #228B22"># of streaming data into a model</span>
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'data'</span>):
|
||||
<span style="color: #658b00">self</span>.X = tf.placeholder(tf.float32, shape=(<span style="color: #658b00">None</span>, <span style="color: #658b00">self</span>.n_features), name=<span style="color: #CD5555">'X_data'</span>)
|
||||
<span style="color: #658b00">self</span>.Y = tf.placeholder(tf.float32, shape=(<span style="color: #658b00">None</span>, <span style="color: #658b00">self</span>.n_categories), name=<span style="color: #CD5555">'Y_data'</span>)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_DNN</span>(<span style="color: #658b00">self</span>):
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'DNN'</span>):
|
||||
<span style="color: #228B22"># the weights are stored to calculate regularization loss later</span>
|
||||
|
||||
<span style="color: #228B22"># Fully connected layer 1</span>
|
||||
<span style="color: #658b00">self</span>.W_fc1 = <span style="color: #658b00">self</span>.weight_variable([<span style="color: #658b00">self</span>.n_features, <span style="color: #658b00">self</span>.n_neurons_layer1], name=<span style="color: #CD5555">'fc1'</span>, dtype=tf.float32)
|
||||
b_fc1 = <span style="color: #658b00">self</span>.bias_variable([<span style="color: #658b00">self</span>.n_neurons_layer1], name=<span style="color: #CD5555">'fc1'</span>, dtype=tf.float32)
|
||||
a_fc1 = tf.nn.sigmoid(tf.matmul(<span style="color: #658b00">self</span>.X, <span style="color: #658b00">self</span>.W_fc1) + b_fc1)
|
||||
|
||||
<span style="color: #228B22"># Fully connected layer 2</span>
|
||||
<span style="color: #658b00">self</span>.W_fc2 = <span style="color: #658b00">self</span>.weight_variable([<span style="color: #658b00">self</span>.n_neurons_layer1, <span style="color: #658b00">self</span>.n_neurons_layer2], name=<span style="color: #CD5555">'fc2'</span>, dtype=tf.float32)
|
||||
b_fc2 = <span style="color: #658b00">self</span>.bias_variable([<span style="color: #658b00">self</span>.n_neurons_layer2], name=<span style="color: #CD5555">'fc2'</span>, dtype=tf.float32)
|
||||
a_fc2 = tf.nn.sigmoid(tf.matmul(a_fc1, <span style="color: #658b00">self</span>.W_fc2) + b_fc2)
|
||||
|
||||
<span style="color: #228B22"># Output layer</span>
|
||||
<span style="color: #658b00">self</span>.W_out = <span style="color: #658b00">self</span>.weight_variable([<span style="color: #658b00">self</span>.n_neurons_layer2, <span style="color: #658b00">self</span>.n_categories], name=<span style="color: #CD5555">'out'</span>, dtype=tf.float32)
|
||||
b_out = <span style="color: #658b00">self</span>.bias_variable([<span style="color: #658b00">self</span>.n_categories], name=<span style="color: #CD5555">'out'</span>, dtype=tf.float32)
|
||||
<span style="color: #658b00">self</span>.z_out = tf.matmul(a_fc2, <span style="color: #658b00">self</span>.W_out) + b_out
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_loss</span>(<span style="color: #658b00">self</span>):
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'loss'</span>):
|
||||
softmax_loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits_v2(labels=<span style="color: #658b00">self</span>.Y, logits=<span style="color: #658b00">self</span>.z_out))
|
||||
|
||||
regularizer_loss_fc1 = tf.nn.l2_loss(<span style="color: #658b00">self</span>.W_fc1)
|
||||
regularizer_loss_fc2 = tf.nn.l2_loss(<span style="color: #658b00">self</span>.W_fc2)
|
||||
regularizer_loss_out = tf.nn.l2_loss(<span style="color: #658b00">self</span>.W_out)
|
||||
regularizer_loss = <span style="color: #658b00">self</span>.lmbd*(regularizer_loss_fc1 + regularizer_loss_fc2 + regularizer_loss_out)
|
||||
|
||||
<span style="color: #658b00">self</span>.loss = softmax_loss + regularizer_loss
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_accuracy</span>(<span style="color: #658b00">self</span>):
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'accuracy'</span>):
|
||||
probabilities = tf.nn.softmax(<span style="color: #658b00">self</span>.z_out)
|
||||
predictions = tf.argmax(probabilities, axis=<span style="color: #B452CD">1</span>)
|
||||
labels = tf.argmax(<span style="color: #658b00">self</span>.Y, axis=<span style="color: #B452CD">1</span>)
|
||||
|
||||
correct_predictions = tf.equal(predictions, labels)
|
||||
correct_predictions = tf.cast(correct_predictions, tf.float32)
|
||||
<span style="color: #658b00">self</span>.accuracy = tf.reduce_mean(correct_predictions)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_optimiser</span>(<span style="color: #658b00">self</span>):
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'optimizer'</span>):
|
||||
<span style="color: #658b00">self</span>.optimizer = tf.train.GradientDescentOptimizer(learning_rate=<span style="color: #658b00">self</span>.eta).minimize(<span style="color: #658b00">self</span>.loss, global_step=<span style="color: #658b00">self</span>.global_step)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">weight_variable</span>(<span style="color: #658b00">self</span>, shape, name=<span style="color: #CD5555">''</span>, dtype=tf.float32):
|
||||
initial = tf.truncated_normal(shape, stddev=<span style="color: #B452CD">0.1</span>)
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> tf.Variable(initial, name=name, dtype=dtype)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">bias_variable</span>(<span style="color: #658b00">self</span>, shape, name=<span style="color: #CD5555">''</span>, dtype=tf.float32):
|
||||
initial = tf.constant(<span style="color: #B452CD">0.1</span>, shape=shape)
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> tf.Variable(initial, name=name, dtype=dtype)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">fit</span>(<span style="color: #658b00">self</span>):
|
||||
data_indices = np.arange(<span style="color: #658b00">self</span>.n_inputs)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.Session() <span style="color: #8B008B; font-weight: bold">as</span> sess:
|
||||
sess.run(tf.global_variables_initializer())
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">self</span>.epochs):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">self</span>.iterations):
|
||||
chosen_datapoints = np.random.choice(data_indices, size=<span style="color: #658b00">self</span>.batch_size, replace=<span style="color: #658b00">False</span>)
|
||||
batch_X, batch_Y = <span style="color: #658b00">self</span>.X_train[chosen_datapoints], <span style="color: #658b00">self</span>.Y_train[chosen_datapoints]
|
||||
|
||||
sess.run([DNN.loss, DNN.optimizer],
|
||||
feed_dict={DNN.X: batch_X,
|
||||
DNN.Y: batch_Y})
|
||||
accuracy = sess.run(DNN.accuracy,
|
||||
feed_dict={DNN.X: batch_X,
|
||||
DNN.Y: batch_Y})
|
||||
step = sess.run(DNN.global_step)
|
||||
|
||||
<span style="color: #658b00">self</span>.train_loss, <span style="color: #658b00">self</span>.train_accuracy = sess.run([DNN.loss, DNN.accuracy],
|
||||
feed_dict={DNN.X: <span style="color: #658b00">self</span>.X_train,
|
||||
DNN.Y: <span style="color: #658b00">self</span>.Y_train})
|
||||
|
||||
<span style="color: #658b00">self</span>.test_loss, <span style="color: #658b00">self</span>.test_accuracy = sess.run([DNN.loss, DNN.accuracy],
|
||||
feed_dict={DNN.X: <span style="color: #658b00">self</span>.X_test,
|
||||
DNN.Y: <span style="color: #658b00">self</span>.Y_test})
|
||||
</pre></div>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec53">Optimizing and using gradient descent </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>epochs = <span style="color: #B452CD">100</span>
|
||||
batch_size = <span style="color: #B452CD">100</span>
|
||||
n_neurons_layer1 = <span style="color: #B452CD">100</span>
|
||||
n_neurons_layer2 = <span style="color: #B452CD">50</span>
|
||||
n_categories = <span style="color: #B452CD">10</span>
|
||||
|
||||
eta_vals = np.logspace(-<span style="color: #B452CD">5</span>, <span style="color: #B452CD">1</span>, <span style="color: #B452CD">7</span>)
|
||||
lmbd_vals = np.logspace(-<span style="color: #B452CD">5</span>, <span style="color: #B452CD">1</span>, <span style="color: #B452CD">7</span>)
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>DNN_tf = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)), dtype=<span style="color: #658b00">object</span>)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i, eta <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(eta_vals):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j, lmbd <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(lmbd_vals):
|
||||
DNN = NeuralNetworkTensorflow(X_train, Y_train, X_test, Y_test,
|
||||
n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
epochs=epochs, batch_size=batch_size, eta=eta, lmbd=lmbd)
|
||||
DNN.fit()
|
||||
|
||||
DNN_tf[i][j] = DNN
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Learning rate = "</span>, eta)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Test accuracy: %.3f"</span> % DNN.test_accuracy)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>()
|
||||
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># optional</span>
|
||||
<span style="color: #228B22"># visual representation of grid search</span>
|
||||
<span style="color: #228B22"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
|
||||
|
||||
sns.set()
|
||||
|
||||
train_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
test_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(eta_vals)):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(lmbd_vals)):
|
||||
DNN = DNN_tf[i][j]
|
||||
|
||||
train_accuracy[i][j] = DNN.train_accuracy
|
||||
test_accuracy[i][j] = DNN.test_accuracy
|
||||
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(train_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Training Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(test_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Test Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># optional</span>
|
||||
<span style="color: #228B22"># we can use log files to visualize our graph in Tensorboard</span>
|
||||
writer = tf.summary.FileWriter(<span style="color: #CD5555">'logs/'</span>)
|
||||
writer.add_graph(tf.get_default_graph())
|
||||
</pre></div>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec54">Using Keras </h2>
|
||||
|
||||
<p>
|
||||
Keras is a high level <a href="https://en.wikipedia.org/wiki/Application_programming_interface" target="_blank">neural network</a>
|
||||
that supports Tensorflow, CTNK and Theano as backends.
|
||||
If you have Tensorflow installed Keras is available through the <em>tf.keras</em> module.
|
||||
If you have Anaconda installed you may run the following command
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>conda install keras
|
||||
</pre></div>
|
||||
<p>
|
||||
Alternatively, if you have Tensorflow or one of the other supported backends install you may use the pip package manager:
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>pip3 install keras
|
||||
</pre></div>
|
||||
<p>
|
||||
or look up the <a href="https://keras.io/" target="_blank">instructions here</a>.
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.models</span> <span style="color: #8B008B; font-weight: bold">import</span> Sequential
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.layers</span> <span style="color: #8B008B; font-weight: bold">import</span> Dense
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.regularizers</span> <span style="color: #8B008B; font-weight: bold">import</span> l2
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.optimizers</span> <span style="color: #8B008B; font-weight: bold">import</span> SGD
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_neural_network_keras</span>(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
|
||||
model = Sequential()
|
||||
model.add(Dense(n_neurons_layer1, activation=<span style="color: #CD5555">'sigmoid'</span>, kernel_regularizer=l2(lmbd)))
|
||||
model.add(Dense(n_neurons_layer2, activation=<span style="color: #CD5555">'sigmoid'</span>, kernel_regularizer=l2(lmbd)))
|
||||
model.add(Dense(n_categories, activation=<span style="color: #CD5555">'softmax'</span>))
|
||||
|
||||
sgd = SGD(lr=eta)
|
||||
model.compile(loss=<span style="color: #CD5555">'categorical_crossentropy'</span>, optimizer=sgd, metrics=[<span style="color: #CD5555">'accuracy'</span>])
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> model
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>DNN_keras = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)), dtype=<span style="color: #658b00">object</span>)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i, eta <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(eta_vals):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j, lmbd <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(lmbd_vals):
|
||||
DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
eta=eta, lmbd=lmbd)
|
||||
DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=<span style="color: #B452CD">0</span>)
|
||||
scores = DNN.evaluate(X_test, Y_test)
|
||||
|
||||
DNN_keras[i][j] = DNN
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Learning rate = "</span>, eta)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Test accuracy: %.3f"</span> % scores[<span style="color: #B452CD">1</span>])
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># optional</span>
|
||||
<span style="color: #228B22"># visual representation of grid search</span>
|
||||
<span style="color: #228B22"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
|
||||
|
||||
sns.set()
|
||||
|
||||
train_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
test_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(eta_vals)):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(lmbd_vals)):
|
||||
DNN = DNN_keras[i][j]
|
||||
|
||||
train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[<span style="color: #B452CD">1</span>]
|
||||
test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[<span style="color: #B452CD">1</span>]
|
||||
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(train_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Training Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(test_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Test Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
</pre></div>
|
||||
</section>
|
||||
|
||||
|
||||
|
||||
@@ -135,7 +135,15 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -2175,8 +2183,453 @@ plt.show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec49">And then with Tensorflow </h2>
|
||||
<h2 id="___sec49">Building neural networks in Tensorflow and Keras </h2>
|
||||
|
||||
<p>
|
||||
Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn
|
||||
and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
|
||||
and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.
|
||||
|
||||
<p>
|
||||
In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite
|
||||
clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or
|
||||
NumPy arrays.
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec50">Tensorflow </h2>
|
||||
|
||||
<p>
|
||||
Tensorflow is an open source library machine learning library
|
||||
developed by the Google Brain team for internal use. It was released
|
||||
under the Apache 2.0 open source license in November 9, 2015.
|
||||
|
||||
<p>
|
||||
Tensorflow is a computational framework that allows you to construct
|
||||
machine learning models at different levels of abstraction, from
|
||||
high-level, object-oriented APIs like Keras, down to the C++ kernels
|
||||
that Tensorflow is built upon. The higher levels of abstraction are
|
||||
simpler to use, but less flexible, and our choice of implementation
|
||||
should reflect the problems we are trying to solve.
|
||||
|
||||
<p>
|
||||
<a href="https://www.tensorflow.org/guide/graphs" target="_blank">Tensorflow uses</a> so-called graphs to represent your computation
|
||||
in terms of the dependencies between individual operations, such that you first build a Tensorflow <em>graph</em>
|
||||
to represent your model, and then create a Tensorflow <em>session</em> to run the graph.
|
||||
|
||||
<p>
|
||||
In this guide we will analyze the same data as we did in our NumPy and
|
||||
scikit-learn tutorial, gathered from the MNIST database of images. We
|
||||
will give an introduction to the lower level Python Application
|
||||
Program Interfaces (APIs), and see how we use them to build our graph.
|
||||
Then we will build (effectively) the same graph in Keras, to see just
|
||||
how simple solving a machine learning problem can be.
|
||||
|
||||
<p>
|
||||
To install tensorflow on Unix/Linux systems, use pip as
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>pip3 install tensorflow
|
||||
</pre></div>
|
||||
<p>
|
||||
and/or if you use <b>anaconda</b>, just write (or install from the graphical user interface)
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>conda install tensorflow
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec51">Collect and pre-process data </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># import necessary packages</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn</span> <span style="color: #8B008B; font-weight: bold">import</span> datasets
|
||||
|
||||
|
||||
<span style="color: #228B22"># ensure the same random numbers appear every time</span>
|
||||
np.random.seed(<span style="color: #B452CD">0</span>)
|
||||
|
||||
<span style="color: #228B22"># display images in notebook</span>
|
||||
%matplotlib inline
|
||||
plt.rcParams[<span style="color: #CD5555">'figure.figsize'</span>] = (<span style="color: #B452CD">12</span>,<span style="color: #B452CD">12</span>)
|
||||
|
||||
|
||||
<span style="color: #228B22"># download MNIST dataset</span>
|
||||
digits = datasets.load_digits()
|
||||
|
||||
<span style="color: #228B22"># define inputs and labels</span>
|
||||
inputs = digits.images
|
||||
labels = digits.target
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"inputs = (n_inputs, pixel_width, pixel_height) = "</span> + <span style="color: #658b00">str</span>(inputs.shape))
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"labels = (n_inputs) = "</span> + <span style="color: #658b00">str</span>(labels.shape))
|
||||
|
||||
|
||||
<span style="color: #228B22"># flatten the image</span>
|
||||
<span style="color: #228B22"># the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64</span>
|
||||
n_inputs = <span style="color: #658b00">len</span>(inputs)
|
||||
inputs = inputs.reshape(n_inputs, -<span style="color: #B452CD">1</span>)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"X = (n_inputs, n_features) = "</span> + <span style="color: #658b00">str</span>(inputs.shape))
|
||||
|
||||
|
||||
<span style="color: #228B22"># choose some random images to display</span>
|
||||
indices = np.arange(n_inputs)
|
||||
random_indices = np.random.choice(indices, size=<span style="color: #B452CD">5</span>)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i, image <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(digits.images[random_indices]):
|
||||
plt.subplot(<span style="color: #B452CD">1</span>, <span style="color: #B452CD">5</span>, i+<span style="color: #B452CD">1</span>)
|
||||
plt.axis(<span style="color: #CD5555">'off'</span>)
|
||||
plt.imshow(image, cmap=plt.cm.gray_r, interpolation=<span style="color: #CD5555">'nearest'</span>)
|
||||
plt.title(<span style="color: #CD5555">"Label: %d"</span> % digits.target[random_indices[i]])
|
||||
plt.show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.utils</span> <span style="color: #8B008B; font-weight: bold">import</span> to_categorical
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> train_test_split
|
||||
|
||||
<span style="color: #228B22"># one-hot representation of labels</span>
|
||||
labels = to_categorical(labels)
|
||||
|
||||
<span style="color: #228B22"># split into train and test data</span>
|
||||
train_size = <span style="color: #B452CD">0.8</span>
|
||||
test_size = <span style="color: #B452CD">1</span> - train_size
|
||||
X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
|
||||
test_size=test_size)
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec52">Using TensorFlow backend </h2>
|
||||
|
||||
<ol>
|
||||
<li> Define model and architecture</li>
|
||||
<li> Choose cost function and optimizer</li>
|
||||
</ol>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">tensorflow</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">tf</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">class</span> <span style="color: #008b45; font-weight: bold">NeuralNetworkTensorflow</span>:
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">__init__</span>(
|
||||
<span style="color: #658b00">self</span>,
|
||||
X_train,
|
||||
Y_train,
|
||||
X_test,
|
||||
Y_test,
|
||||
n_neurons_layer1=<span style="color: #B452CD">100</span>,
|
||||
n_neurons_layer2=<span style="color: #B452CD">50</span>,
|
||||
n_categories=<span style="color: #B452CD">2</span>,
|
||||
epochs=<span style="color: #B452CD">10</span>,
|
||||
batch_size=<span style="color: #B452CD">100</span>,
|
||||
eta=<span style="color: #B452CD">0.1</span>,
|
||||
lmbd=<span style="color: #B452CD">0.0</span>,
|
||||
):
|
||||
|
||||
<span style="color: #228B22"># keep track of number of steps</span>
|
||||
<span style="color: #658b00">self</span>.global_step = tf.Variable(<span style="color: #B452CD">0</span>, dtype=tf.int32, trainable=<span style="color: #658b00">False</span>, name=<span style="color: #CD5555">'global_step'</span>)
|
||||
|
||||
<span style="color: #658b00">self</span>.X_train = X_train
|
||||
<span style="color: #658b00">self</span>.Y_train = Y_train
|
||||
<span style="color: #658b00">self</span>.X_test = X_test
|
||||
<span style="color: #658b00">self</span>.Y_test = Y_test
|
||||
|
||||
<span style="color: #658b00">self</span>.n_inputs = X_train.shape[<span style="color: #B452CD">0</span>]
|
||||
<span style="color: #658b00">self</span>.n_features = X_train.shape[<span style="color: #B452CD">1</span>]
|
||||
<span style="color: #658b00">self</span>.n_neurons_layer1 = n_neurons_layer1
|
||||
<span style="color: #658b00">self</span>.n_neurons_layer2 = n_neurons_layer2
|
||||
<span style="color: #658b00">self</span>.n_categories = n_categories
|
||||
|
||||
<span style="color: #658b00">self</span>.epochs = epochs
|
||||
<span style="color: #658b00">self</span>.batch_size = batch_size
|
||||
<span style="color: #658b00">self</span>.iterations = <span style="color: #658b00">self</span>.n_inputs // <span style="color: #658b00">self</span>.batch_size
|
||||
<span style="color: #658b00">self</span>.eta = eta
|
||||
<span style="color: #658b00">self</span>.lmbd = lmbd
|
||||
|
||||
<span style="color: #228B22"># build network piece by piece</span>
|
||||
<span style="color: #228B22"># name scopes (with) are used to enforce creation of new variables</span>
|
||||
<span style="color: #228B22"># https://www.tensorflow.org/guide/variables</span>
|
||||
<span style="color: #658b00">self</span>.create_placeholders()
|
||||
<span style="color: #658b00">self</span>.create_DNN()
|
||||
<span style="color: #658b00">self</span>.create_loss()
|
||||
<span style="color: #658b00">self</span>.create_optimiser()
|
||||
<span style="color: #658b00">self</span>.create_accuracy()
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_placeholders</span>(<span style="color: #658b00">self</span>):
|
||||
<span style="color: #228B22"># placeholders are fine here, but "Datasets" are the preferred method</span>
|
||||
<span style="color: #228B22"># of streaming data into a model</span>
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'data'</span>):
|
||||
<span style="color: #658b00">self</span>.X = tf.placeholder(tf.float32, shape=(<span style="color: #658b00">None</span>, <span style="color: #658b00">self</span>.n_features), name=<span style="color: #CD5555">'X_data'</span>)
|
||||
<span style="color: #658b00">self</span>.Y = tf.placeholder(tf.float32, shape=(<span style="color: #658b00">None</span>, <span style="color: #658b00">self</span>.n_categories), name=<span style="color: #CD5555">'Y_data'</span>)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_DNN</span>(<span style="color: #658b00">self</span>):
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'DNN'</span>):
|
||||
<span style="color: #228B22"># the weights are stored to calculate regularization loss later</span>
|
||||
|
||||
<span style="color: #228B22"># Fully connected layer 1</span>
|
||||
<span style="color: #658b00">self</span>.W_fc1 = <span style="color: #658b00">self</span>.weight_variable([<span style="color: #658b00">self</span>.n_features, <span style="color: #658b00">self</span>.n_neurons_layer1], name=<span style="color: #CD5555">'fc1'</span>, dtype=tf.float32)
|
||||
b_fc1 = <span style="color: #658b00">self</span>.bias_variable([<span style="color: #658b00">self</span>.n_neurons_layer1], name=<span style="color: #CD5555">'fc1'</span>, dtype=tf.float32)
|
||||
a_fc1 = tf.nn.sigmoid(tf.matmul(<span style="color: #658b00">self</span>.X, <span style="color: #658b00">self</span>.W_fc1) + b_fc1)
|
||||
|
||||
<span style="color: #228B22"># Fully connected layer 2</span>
|
||||
<span style="color: #658b00">self</span>.W_fc2 = <span style="color: #658b00">self</span>.weight_variable([<span style="color: #658b00">self</span>.n_neurons_layer1, <span style="color: #658b00">self</span>.n_neurons_layer2], name=<span style="color: #CD5555">'fc2'</span>, dtype=tf.float32)
|
||||
b_fc2 = <span style="color: #658b00">self</span>.bias_variable([<span style="color: #658b00">self</span>.n_neurons_layer2], name=<span style="color: #CD5555">'fc2'</span>, dtype=tf.float32)
|
||||
a_fc2 = tf.nn.sigmoid(tf.matmul(a_fc1, <span style="color: #658b00">self</span>.W_fc2) + b_fc2)
|
||||
|
||||
<span style="color: #228B22"># Output layer</span>
|
||||
<span style="color: #658b00">self</span>.W_out = <span style="color: #658b00">self</span>.weight_variable([<span style="color: #658b00">self</span>.n_neurons_layer2, <span style="color: #658b00">self</span>.n_categories], name=<span style="color: #CD5555">'out'</span>, dtype=tf.float32)
|
||||
b_out = <span style="color: #658b00">self</span>.bias_variable([<span style="color: #658b00">self</span>.n_categories], name=<span style="color: #CD5555">'out'</span>, dtype=tf.float32)
|
||||
<span style="color: #658b00">self</span>.z_out = tf.matmul(a_fc2, <span style="color: #658b00">self</span>.W_out) + b_out
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_loss</span>(<span style="color: #658b00">self</span>):
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'loss'</span>):
|
||||
softmax_loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits_v2(labels=<span style="color: #658b00">self</span>.Y, logits=<span style="color: #658b00">self</span>.z_out))
|
||||
|
||||
regularizer_loss_fc1 = tf.nn.l2_loss(<span style="color: #658b00">self</span>.W_fc1)
|
||||
regularizer_loss_fc2 = tf.nn.l2_loss(<span style="color: #658b00">self</span>.W_fc2)
|
||||
regularizer_loss_out = tf.nn.l2_loss(<span style="color: #658b00">self</span>.W_out)
|
||||
regularizer_loss = <span style="color: #658b00">self</span>.lmbd*(regularizer_loss_fc1 + regularizer_loss_fc2 + regularizer_loss_out)
|
||||
|
||||
<span style="color: #658b00">self</span>.loss = softmax_loss + regularizer_loss
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_accuracy</span>(<span style="color: #658b00">self</span>):
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'accuracy'</span>):
|
||||
probabilities = tf.nn.softmax(<span style="color: #658b00">self</span>.z_out)
|
||||
predictions = tf.argmax(probabilities, axis=<span style="color: #B452CD">1</span>)
|
||||
labels = tf.argmax(<span style="color: #658b00">self</span>.Y, axis=<span style="color: #B452CD">1</span>)
|
||||
|
||||
correct_predictions = tf.equal(predictions, labels)
|
||||
correct_predictions = tf.cast(correct_predictions, tf.float32)
|
||||
<span style="color: #658b00">self</span>.accuracy = tf.reduce_mean(correct_predictions)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_optimiser</span>(<span style="color: #658b00">self</span>):
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'optimizer'</span>):
|
||||
<span style="color: #658b00">self</span>.optimizer = tf.train.GradientDescentOptimizer(learning_rate=<span style="color: #658b00">self</span>.eta).minimize(<span style="color: #658b00">self</span>.loss, global_step=<span style="color: #658b00">self</span>.global_step)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">weight_variable</span>(<span style="color: #658b00">self</span>, shape, name=<span style="color: #CD5555">''</span>, dtype=tf.float32):
|
||||
initial = tf.truncated_normal(shape, stddev=<span style="color: #B452CD">0.1</span>)
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> tf.Variable(initial, name=name, dtype=dtype)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">bias_variable</span>(<span style="color: #658b00">self</span>, shape, name=<span style="color: #CD5555">''</span>, dtype=tf.float32):
|
||||
initial = tf.constant(<span style="color: #B452CD">0.1</span>, shape=shape)
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> tf.Variable(initial, name=name, dtype=dtype)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">fit</span>(<span style="color: #658b00">self</span>):
|
||||
data_indices = np.arange(<span style="color: #658b00">self</span>.n_inputs)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.Session() <span style="color: #8B008B; font-weight: bold">as</span> sess:
|
||||
sess.run(tf.global_variables_initializer())
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">self</span>.epochs):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">self</span>.iterations):
|
||||
chosen_datapoints = np.random.choice(data_indices, size=<span style="color: #658b00">self</span>.batch_size, replace=<span style="color: #658b00">False</span>)
|
||||
batch_X, batch_Y = <span style="color: #658b00">self</span>.X_train[chosen_datapoints], <span style="color: #658b00">self</span>.Y_train[chosen_datapoints]
|
||||
|
||||
sess.run([DNN.loss, DNN.optimizer],
|
||||
feed_dict={DNN.X: batch_X,
|
||||
DNN.Y: batch_Y})
|
||||
accuracy = sess.run(DNN.accuracy,
|
||||
feed_dict={DNN.X: batch_X,
|
||||
DNN.Y: batch_Y})
|
||||
step = sess.run(DNN.global_step)
|
||||
|
||||
<span style="color: #658b00">self</span>.train_loss, <span style="color: #658b00">self</span>.train_accuracy = sess.run([DNN.loss, DNN.accuracy],
|
||||
feed_dict={DNN.X: <span style="color: #658b00">self</span>.X_train,
|
||||
DNN.Y: <span style="color: #658b00">self</span>.Y_train})
|
||||
|
||||
<span style="color: #658b00">self</span>.test_loss, <span style="color: #658b00">self</span>.test_accuracy = sess.run([DNN.loss, DNN.accuracy],
|
||||
feed_dict={DNN.X: <span style="color: #658b00">self</span>.X_test,
|
||||
DNN.Y: <span style="color: #658b00">self</span>.Y_test})
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec53">Optimizing and using gradient descent </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>epochs = <span style="color: #B452CD">100</span>
|
||||
batch_size = <span style="color: #B452CD">100</span>
|
||||
n_neurons_layer1 = <span style="color: #B452CD">100</span>
|
||||
n_neurons_layer2 = <span style="color: #B452CD">50</span>
|
||||
n_categories = <span style="color: #B452CD">10</span>
|
||||
|
||||
eta_vals = np.logspace(-<span style="color: #B452CD">5</span>, <span style="color: #B452CD">1</span>, <span style="color: #B452CD">7</span>)
|
||||
lmbd_vals = np.logspace(-<span style="color: #B452CD">5</span>, <span style="color: #B452CD">1</span>, <span style="color: #B452CD">7</span>)
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>DNN_tf = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)), dtype=<span style="color: #658b00">object</span>)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i, eta <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(eta_vals):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j, lmbd <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(lmbd_vals):
|
||||
DNN = NeuralNetworkTensorflow(X_train, Y_train, X_test, Y_test,
|
||||
n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
epochs=epochs, batch_size=batch_size, eta=eta, lmbd=lmbd)
|
||||
DNN.fit()
|
||||
|
||||
DNN_tf[i][j] = DNN
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Learning rate = "</span>, eta)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Test accuracy: %.3f"</span> % DNN.test_accuracy)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>()
|
||||
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># optional</span>
|
||||
<span style="color: #228B22"># visual representation of grid search</span>
|
||||
<span style="color: #228B22"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
|
||||
|
||||
sns.set()
|
||||
|
||||
train_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
test_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(eta_vals)):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(lmbd_vals)):
|
||||
DNN = DNN_tf[i][j]
|
||||
|
||||
train_accuracy[i][j] = DNN.train_accuracy
|
||||
test_accuracy[i][j] = DNN.test_accuracy
|
||||
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(train_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Training Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(test_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Test Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># optional</span>
|
||||
<span style="color: #228B22"># we can use log files to visualize our graph in Tensorboard</span>
|
||||
writer = tf.summary.FileWriter(<span style="color: #CD5555">'logs/'</span>)
|
||||
writer.add_graph(tf.get_default_graph())
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec54">Using Keras </h2>
|
||||
|
||||
<p>
|
||||
Keras is a high level <a href="https://en.wikipedia.org/wiki/Application_programming_interface" target="_blank">neural network</a>
|
||||
that supports Tensorflow, CTNK and Theano as backends.
|
||||
If you have Tensorflow installed Keras is available through the <em>tf.keras</em> module.
|
||||
If you have Anaconda installed you may run the following command
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>conda install keras
|
||||
</pre></div>
|
||||
<p>
|
||||
Alternatively, if you have Tensorflow or one of the other supported backends install you may use the pip package manager:
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>pip3 install keras
|
||||
</pre></div>
|
||||
<p>
|
||||
or look up the <a href="https://keras.io/" target="_blank">instructions here</a>.
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.models</span> <span style="color: #8B008B; font-weight: bold">import</span> Sequential
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.layers</span> <span style="color: #8B008B; font-weight: bold">import</span> Dense
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.regularizers</span> <span style="color: #8B008B; font-weight: bold">import</span> l2
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.optimizers</span> <span style="color: #8B008B; font-weight: bold">import</span> SGD
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_neural_network_keras</span>(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
|
||||
model = Sequential()
|
||||
model.add(Dense(n_neurons_layer1, activation=<span style="color: #CD5555">'sigmoid'</span>, kernel_regularizer=l2(lmbd)))
|
||||
model.add(Dense(n_neurons_layer2, activation=<span style="color: #CD5555">'sigmoid'</span>, kernel_regularizer=l2(lmbd)))
|
||||
model.add(Dense(n_categories, activation=<span style="color: #CD5555">'softmax'</span>))
|
||||
|
||||
sgd = SGD(lr=eta)
|
||||
model.compile(loss=<span style="color: #CD5555">'categorical_crossentropy'</span>, optimizer=sgd, metrics=[<span style="color: #CD5555">'accuracy'</span>])
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> model
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>DNN_keras = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)), dtype=<span style="color: #658b00">object</span>)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i, eta <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(eta_vals):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j, lmbd <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(lmbd_vals):
|
||||
DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
eta=eta, lmbd=lmbd)
|
||||
DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=<span style="color: #B452CD">0</span>)
|
||||
scores = DNN.evaluate(X_test, Y_test)
|
||||
|
||||
DNN_keras[i][j] = DNN
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Learning rate = "</span>, eta)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Test accuracy: %.3f"</span> % scores[<span style="color: #B452CD">1</span>])
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># optional</span>
|
||||
<span style="color: #228B22"># visual representation of grid search</span>
|
||||
<span style="color: #228B22"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
|
||||
|
||||
sns.set()
|
||||
|
||||
train_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
test_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(eta_vals)):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(lmbd_vals)):
|
||||
DNN = DNN_keras[i][j]
|
||||
|
||||
train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[<span style="color: #B452CD">1</span>]
|
||||
test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[<span style="color: #B452CD">1</span>]
|
||||
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(train_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Training Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(test_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Test Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -140,7 +140,15 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
None,
|
||||
'___sec47'),
|
||||
('scikit-learn implementation', 2, None, '___sec48'),
|
||||
('And then with Tensorflow', 2, None, '___sec49')]}
|
||||
('Building neural networks in Tensorflow and Keras',
|
||||
2,
|
||||
None,
|
||||
'___sec49'),
|
||||
('Tensorflow', 2, None, '___sec50'),
|
||||
('Collect and pre-process data', 2, None, '___sec51'),
|
||||
('Using TensorFlow backend', 2, None, '___sec52'),
|
||||
('Optimizing and using gradient descent', 2, None, '___sec53'),
|
||||
('Using Keras', 2, None, '___sec54')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -2180,8 +2188,453 @@ plt<span style="color: #666666">.</span>show()
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec49">And then with Tensorflow </h2>
|
||||
<h2 id="___sec49">Building neural networks in Tensorflow and Keras </h2>
|
||||
|
||||
<p>
|
||||
Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn
|
||||
and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
|
||||
and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.
|
||||
|
||||
<p>
|
||||
In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite
|
||||
clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or
|
||||
NumPy arrays.
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec50">Tensorflow </h2>
|
||||
|
||||
<p>
|
||||
Tensorflow is an open source library machine learning library
|
||||
developed by the Google Brain team for internal use. It was released
|
||||
under the Apache 2.0 open source license in November 9, 2015.
|
||||
|
||||
<p>
|
||||
Tensorflow is a computational framework that allows you to construct
|
||||
machine learning models at different levels of abstraction, from
|
||||
high-level, object-oriented APIs like Keras, down to the C++ kernels
|
||||
that Tensorflow is built upon. The higher levels of abstraction are
|
||||
simpler to use, but less flexible, and our choice of implementation
|
||||
should reflect the problems we are trying to solve.
|
||||
|
||||
<p>
|
||||
<a href="https://www.tensorflow.org/guide/graphs" target="_blank">Tensorflow uses</a> so-called graphs to represent your computation
|
||||
in terms of the dependencies between individual operations, such that you first build a Tensorflow <em>graph</em>
|
||||
to represent your model, and then create a Tensorflow <em>session</em> to run the graph.
|
||||
|
||||
<p>
|
||||
In this guide we will analyze the same data as we did in our NumPy and
|
||||
scikit-learn tutorial, gathered from the MNIST database of images. We
|
||||
will give an introduction to the lower level Python Application
|
||||
Program Interfaces (APIs), and see how we use them to build our graph.
|
||||
Then we will build (effectively) the same graph in Keras, to see just
|
||||
how simple solving a machine learning problem can be.
|
||||
|
||||
<p>
|
||||
To install tensorflow on Unix/Linux systems, use pip as
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pip3 install tensorflow
|
||||
</pre></div>
|
||||
<p>
|
||||
and/or if you use <b>anaconda</b>, just write (or install from the graphical user interface)
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>conda install tensorflow
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec51">Collect and pre-process data </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># import necessary packages</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> datasets
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># ensure the same random numbers appear every time</span>
|
||||
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">0</span>)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># display images in notebook</span>
|
||||
<span style="color: #666666">%</span>matplotlib inline
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'figure.figsize'</span>] <span style="color: #666666">=</span> (<span style="color: #666666">12</span>,<span style="color: #666666">12</span>)
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># download MNIST dataset</span>
|
||||
digits <span style="color: #666666">=</span> datasets<span style="color: #666666">.</span>load_digits()
|
||||
|
||||
<span style="color: #408080; font-style: italic"># define inputs and labels</span>
|
||||
inputs <span style="color: #666666">=</span> digits<span style="color: #666666">.</span>images
|
||||
labels <span style="color: #666666">=</span> digits<span style="color: #666666">.</span>target
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"inputs = (n_inputs, pixel_width, pixel_height) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(inputs<span style="color: #666666">.</span>shape))
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"labels = (n_inputs) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(labels<span style="color: #666666">.</span>shape))
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># flatten the image</span>
|
||||
<span style="color: #408080; font-style: italic"># the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64</span>
|
||||
n_inputs <span style="color: #666666">=</span> <span style="color: #008000">len</span>(inputs)
|
||||
inputs <span style="color: #666666">=</span> inputs<span style="color: #666666">.</span>reshape(n_inputs, <span style="color: #666666">-1</span>)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"X = (n_inputs, n_features) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(inputs<span style="color: #666666">.</span>shape))
|
||||
|
||||
|
||||
<span style="color: #408080; font-style: italic"># choose some random images to display</span>
|
||||
indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(n_inputs)
|
||||
random_indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>choice(indices, size<span style="color: #666666">=5</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i, image <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(digits<span style="color: #666666">.</span>images[random_indices]):
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">1</span>, <span style="color: #666666">5</span>, i<span style="color: #666666">+1</span>)
|
||||
plt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">'off'</span>)
|
||||
plt<span style="color: #666666">.</span>imshow(image, cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>gray_r, interpolation<span style="color: #666666">=</span><span style="color: #BA2121">'nearest'</span>)
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Label: </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> digits<span style="color: #666666">.</span>target[random_indices[i]])
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.utils</span> <span style="color: #008000; font-weight: bold">import</span> to_categorical
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
|
||||
|
||||
<span style="color: #408080; font-style: italic"># one-hot representation of labels</span>
|
||||
labels <span style="color: #666666">=</span> to_categorical(labels)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># split into train and test data</span>
|
||||
train_size <span style="color: #666666">=</span> <span style="color: #666666">0.8</span>
|
||||
test_size <span style="color: #666666">=</span> <span style="color: #666666">1</span> <span style="color: #666666">-</span> train_size
|
||||
X_train, X_test, Y_train, Y_test <span style="color: #666666">=</span> train_test_split(inputs, labels, train_size<span style="color: #666666">=</span>train_size,
|
||||
test_size<span style="color: #666666">=</span>test_size)
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec52">Using TensorFlow backend </h2>
|
||||
|
||||
<ol>
|
||||
<li> Define model and architecture</li>
|
||||
<li> Choose cost function and optimizer</li>
|
||||
</ol>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">tensorflow</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">tf</span>
|
||||
|
||||
<span style="color: #008000; font-weight: bold">class</span> <span style="color: #0000FF; font-weight: bold">NeuralNetworkTensorflow</span>:
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">__init__</span>(
|
||||
<span style="color: #008000">self</span>,
|
||||
X_train,
|
||||
Y_train,
|
||||
X_test,
|
||||
Y_test,
|
||||
n_neurons_layer1<span style="color: #666666">=100</span>,
|
||||
n_neurons_layer2<span style="color: #666666">=50</span>,
|
||||
n_categories<span style="color: #666666">=2</span>,
|
||||
epochs<span style="color: #666666">=10</span>,
|
||||
batch_size<span style="color: #666666">=100</span>,
|
||||
eta<span style="color: #666666">=0.1</span>,
|
||||
lmbd<span style="color: #666666">=0.0</span>,
|
||||
):
|
||||
|
||||
<span style="color: #408080; font-style: italic"># keep track of number of steps</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>global_step <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>Variable(<span style="color: #666666">0</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>int32, trainable<span style="color: #666666">=</span><span style="color: #008000">False</span>, name<span style="color: #666666">=</span><span style="color: #BA2121">'global_step'</span>)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>X_train <span style="color: #666666">=</span> X_train
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>Y_train <span style="color: #666666">=</span> Y_train
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>X_test <span style="color: #666666">=</span> X_test
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>Y_test <span style="color: #666666">=</span> Y_test
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>n_inputs <span style="color: #666666">=</span> X_train<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>]
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>n_features <span style="color: #666666">=</span> X_train<span style="color: #666666">.</span>shape[<span style="color: #666666">1</span>]
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1 <span style="color: #666666">=</span> n_neurons_layer1
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2 <span style="color: #666666">=</span> n_neurons_layer2
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories <span style="color: #666666">=</span> n_categories
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>epochs <span style="color: #666666">=</span> epochs
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>batch_size <span style="color: #666666">=</span> batch_size
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>iterations <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>n_inputs <span style="color: #666666">//</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>batch_size
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>eta <span style="color: #666666">=</span> eta
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>lmbd <span style="color: #666666">=</span> lmbd
|
||||
|
||||
<span style="color: #408080; font-style: italic"># build network piece by piece</span>
|
||||
<span style="color: #408080; font-style: italic"># name scopes (with) are used to enforce creation of new variables</span>
|
||||
<span style="color: #408080; font-style: italic"># https://www.tensorflow.org/guide/variables</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>create_placeholders()
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>create_DNN()
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>create_loss()
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>create_optimiser()
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>create_accuracy()
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_placeholders</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #408080; font-style: italic"># placeholders are fine here, but "Datasets" are the preferred method</span>
|
||||
<span style="color: #408080; font-style: italic"># of streaming data into a model</span>
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'data'</span>):
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>X <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>placeholder(tf<span style="color: #666666">.</span>float32, shape<span style="color: #666666">=</span>(<span style="color: #008000">None</span>, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_features), name<span style="color: #666666">=</span><span style="color: #BA2121">'X_data'</span>)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>Y <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>placeholder(tf<span style="color: #666666">.</span>float32, shape<span style="color: #666666">=</span>(<span style="color: #008000">None</span>, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories), name<span style="color: #666666">=</span><span style="color: #BA2121">'Y_data'</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_DNN</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'DNN'</span>):
|
||||
<span style="color: #408080; font-style: italic"># the weights are stored to calculate regularization loss later</span>
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Fully connected layer 1</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc1 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>weight_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_features, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc1'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
b_fc1 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>bias_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc1'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
a_fc1 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>sigmoid(tf<span style="color: #666666">.</span>matmul(<span style="color: #008000">self</span><span style="color: #666666">.</span>X, <span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc1) <span style="color: #666666">+</span> b_fc1)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Fully connected layer 2</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc2 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>weight_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc2'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
b_fc2 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>bias_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc2'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
a_fc2 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>sigmoid(tf<span style="color: #666666">.</span>matmul(a_fc1, <span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc2) <span style="color: #666666">+</span> b_fc2)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Output layer</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>W_out <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>weight_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories], name<span style="color: #666666">=</span><span style="color: #BA2121">'out'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
b_out <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>bias_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories], name<span style="color: #666666">=</span><span style="color: #BA2121">'out'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>z_out <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>matmul(a_fc2, <span style="color: #008000">self</span><span style="color: #666666">.</span>W_out) <span style="color: #666666">+</span> b_out
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_loss</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'loss'</span>):
|
||||
softmax_loss <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>reduce_mean(tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>softmax_cross_entropy_with_logits_v2(labels<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>Y, logits<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>z_out))
|
||||
|
||||
regularizer_loss_fc1 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>l2_loss(<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc1)
|
||||
regularizer_loss_fc2 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>l2_loss(<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc2)
|
||||
regularizer_loss_out <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>l2_loss(<span style="color: #008000">self</span><span style="color: #666666">.</span>W_out)
|
||||
regularizer_loss <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>lmbd<span style="color: #666666">*</span>(regularizer_loss_fc1 <span style="color: #666666">+</span> regularizer_loss_fc2 <span style="color: #666666">+</span> regularizer_loss_out)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>loss <span style="color: #666666">=</span> softmax_loss <span style="color: #666666">+</span> regularizer_loss
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_accuracy</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'accuracy'</span>):
|
||||
probabilities <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>softmax(<span style="color: #008000">self</span><span style="color: #666666">.</span>z_out)
|
||||
predictions <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>argmax(probabilities, axis<span style="color: #666666">=1</span>)
|
||||
labels <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>argmax(<span style="color: #008000">self</span><span style="color: #666666">.</span>Y, axis<span style="color: #666666">=1</span>)
|
||||
|
||||
correct_predictions <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>equal(predictions, labels)
|
||||
correct_predictions <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>cast(correct_predictions, tf<span style="color: #666666">.</span>float32)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>accuracy <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>reduce_mean(correct_predictions)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_optimiser</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'optimizer'</span>):
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>optimizer <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>train<span style="color: #666666">.</span>GradientDescentOptimizer(learning_rate<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>eta)<span style="color: #666666">.</span>minimize(<span style="color: #008000">self</span><span style="color: #666666">.</span>loss, global_step<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>global_step)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">weight_variable</span>(<span style="color: #008000">self</span>, shape, name<span style="color: #666666">=</span><span style="color: #BA2121">''</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32):
|
||||
initial <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>truncated_normal(shape, stddev<span style="color: #666666">=0.1</span>)
|
||||
<span style="color: #008000; font-weight: bold">return</span> tf<span style="color: #666666">.</span>Variable(initial, name<span style="color: #666666">=</span>name, dtype<span style="color: #666666">=</span>dtype)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">bias_variable</span>(<span style="color: #008000">self</span>, shape, name<span style="color: #666666">=</span><span style="color: #BA2121">''</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32):
|
||||
initial <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>constant(<span style="color: #666666">0.1</span>, shape<span style="color: #666666">=</span>shape)
|
||||
<span style="color: #008000; font-weight: bold">return</span> tf<span style="color: #666666">.</span>Variable(initial, name<span style="color: #666666">=</span>name, dtype<span style="color: #666666">=</span>dtype)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">fit</span>(<span style="color: #008000">self</span>):
|
||||
data_indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #008000">self</span><span style="color: #666666">.</span>n_inputs)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>Session() <span style="color: #008000; font-weight: bold">as</span> sess:
|
||||
sess<span style="color: #666666">.</span>run(tf<span style="color: #666666">.</span>global_variables_initializer())
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">self</span><span style="color: #666666">.</span>epochs):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">self</span><span style="color: #666666">.</span>iterations):
|
||||
chosen_datapoints <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>choice(data_indices, size<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>batch_size, replace<span style="color: #666666">=</span><span style="color: #008000">False</span>)
|
||||
batch_X, batch_Y <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>X_train[chosen_datapoints], <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_train[chosen_datapoints]
|
||||
|
||||
sess<span style="color: #666666">.</span>run([DNN<span style="color: #666666">.</span>loss, DNN<span style="color: #666666">.</span>optimizer],
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: batch_X,
|
||||
DNN<span style="color: #666666">.</span>Y: batch_Y})
|
||||
accuracy <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run(DNN<span style="color: #666666">.</span>accuracy,
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: batch_X,
|
||||
DNN<span style="color: #666666">.</span>Y: batch_Y})
|
||||
step <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run(DNN<span style="color: #666666">.</span>global_step)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>train_loss, <span style="color: #008000">self</span><span style="color: #666666">.</span>train_accuracy <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run([DNN<span style="color: #666666">.</span>loss, DNN<span style="color: #666666">.</span>accuracy],
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: <span style="color: #008000">self</span><span style="color: #666666">.</span>X_train,
|
||||
DNN<span style="color: #666666">.</span>Y: <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_train})
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>test_loss, <span style="color: #008000">self</span><span style="color: #666666">.</span>test_accuracy <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run([DNN<span style="color: #666666">.</span>loss, DNN<span style="color: #666666">.</span>accuracy],
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: <span style="color: #008000">self</span><span style="color: #666666">.</span>X_test,
|
||||
DNN<span style="color: #666666">.</span>Y: <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_test})
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec53">Optimizing and using gradient descent </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>epochs <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
batch_size <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
n_neurons_layer1 <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
n_neurons_layer2 <span style="color: #666666">=</span> <span style="color: #666666">50</span>
|
||||
n_categories <span style="color: #666666">=</span> <span style="color: #666666">10</span>
|
||||
|
||||
eta_vals <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-5</span>, <span style="color: #666666">1</span>, <span style="color: #666666">7</span>)
|
||||
lmbd_vals <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-5</span>, <span style="color: #666666">1</span>, <span style="color: #666666">7</span>)
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>DNN_tf <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)), dtype<span style="color: #666666">=</span><span style="color: #008000">object</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i, eta <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(eta_vals):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j, lmbd <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(lmbd_vals):
|
||||
DNN <span style="color: #666666">=</span> NeuralNetworkTensorflow(X_train, Y_train, X_test, Y_test,
|
||||
n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
epochs<span style="color: #666666">=</span>epochs, batch_size<span style="color: #666666">=</span>batch_size, eta<span style="color: #666666">=</span>eta, lmbd<span style="color: #666666">=</span>lmbd)
|
||||
DNN<span style="color: #666666">.</span>fit()
|
||||
|
||||
DNN_tf[i][j] <span style="color: #666666">=</span> DNN
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Learning rate = "</span>, eta)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Test accuracy: </span><span style="color: #BB6688; font-weight: bold">%.3f</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> DNN<span style="color: #666666">.</span>test_accuracy)
|
||||
<span style="color: #008000; font-weight: bold">print</span>()
|
||||
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># optional</span>
|
||||
<span style="color: #408080; font-style: italic"># visual representation of grid search</span>
|
||||
<span style="color: #408080; font-style: italic"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">seaborn</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sns</span>
|
||||
|
||||
sns<span style="color: #666666">.</span>set()
|
||||
|
||||
train_accuracy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)))
|
||||
test_accuracy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(eta_vals)):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(lmbd_vals)):
|
||||
DNN <span style="color: #666666">=</span> DNN_tf[i][j]
|
||||
|
||||
train_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>train_accuracy
|
||||
test_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>test_accuracy
|
||||
|
||||
|
||||
fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(figsize <span style="color: #666666">=</span> (<span style="color: #666666">10</span>, <span style="color: #666666">10</span>))
|
||||
sns<span style="color: #666666">.</span>heatmap(train_accuracy, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>, ax<span style="color: #666666">=</span>ax, cmap<span style="color: #666666">=</span><span style="color: #BA2121">"viridis"</span>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Training Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(figsize <span style="color: #666666">=</span> (<span style="color: #666666">10</span>, <span style="color: #666666">10</span>))
|
||||
sns<span style="color: #666666">.</span>heatmap(test_accuracy, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>, ax<span style="color: #666666">=</span>ax, cmap<span style="color: #666666">=</span><span style="color: #BA2121">"viridis"</span>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Test Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># optional</span>
|
||||
<span style="color: #408080; font-style: italic"># we can use log files to visualize our graph in Tensorboard</span>
|
||||
writer <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>summary<span style="color: #666666">.</span>FileWriter(<span style="color: #BA2121">'logs/'</span>)
|
||||
writer<span style="color: #666666">.</span>add_graph(tf<span style="color: #666666">.</span>get_default_graph())
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec54">Using Keras </h2>
|
||||
|
||||
<p>
|
||||
Keras is a high level <a href="https://en.wikipedia.org/wiki/Application_programming_interface" target="_blank">neural network</a>
|
||||
that supports Tensorflow, CTNK and Theano as backends.
|
||||
If you have Tensorflow installed Keras is available through the <em>tf.keras</em> module.
|
||||
If you have Anaconda installed you may run the following command
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>conda install keras
|
||||
</pre></div>
|
||||
<p>
|
||||
Alternatively, if you have Tensorflow or one of the other supported backends install you may use the pip package manager:
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pip3 install keras
|
||||
</pre></div>
|
||||
<p>
|
||||
or look up the <a href="https://keras.io/" target="_blank">instructions here</a>.
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.models</span> <span style="color: #008000; font-weight: bold">import</span> Sequential
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.layers</span> <span style="color: #008000; font-weight: bold">import</span> Dense
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.regularizers</span> <span style="color: #008000; font-weight: bold">import</span> l2
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.optimizers</span> <span style="color: #008000; font-weight: bold">import</span> SGD
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_neural_network_keras</span>(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
|
||||
model <span style="color: #666666">=</span> Sequential()
|
||||
model<span style="color: #666666">.</span>add(Dense(n_neurons_layer1, activation<span style="color: #666666">=</span><span style="color: #BA2121">'sigmoid'</span>, kernel_regularizer<span style="color: #666666">=</span>l2(lmbd)))
|
||||
model<span style="color: #666666">.</span>add(Dense(n_neurons_layer2, activation<span style="color: #666666">=</span><span style="color: #BA2121">'sigmoid'</span>, kernel_regularizer<span style="color: #666666">=</span>l2(lmbd)))
|
||||
model<span style="color: #666666">.</span>add(Dense(n_categories, activation<span style="color: #666666">=</span><span style="color: #BA2121">'softmax'</span>))
|
||||
|
||||
sgd <span style="color: #666666">=</span> SGD(lr<span style="color: #666666">=</span>eta)
|
||||
model<span style="color: #666666">.</span>compile(loss<span style="color: #666666">=</span><span style="color: #BA2121">'categorical_crossentropy'</span>, optimizer<span style="color: #666666">=</span>sgd, metrics<span style="color: #666666">=</span>[<span style="color: #BA2121">'accuracy'</span>])
|
||||
|
||||
<span style="color: #008000; font-weight: bold">return</span> model
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>DNN_keras <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)), dtype<span style="color: #666666">=</span><span style="color: #008000">object</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i, eta <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(eta_vals):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j, lmbd <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(lmbd_vals):
|
||||
DNN <span style="color: #666666">=</span> create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
eta<span style="color: #666666">=</span>eta, lmbd<span style="color: #666666">=</span>lmbd)
|
||||
DNN<span style="color: #666666">.</span>fit(X_train, Y_train, epochs<span style="color: #666666">=</span>epochs, batch_size<span style="color: #666666">=</span>batch_size, verbose<span style="color: #666666">=0</span>)
|
||||
scores <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>evaluate(X_test, Y_test)
|
||||
|
||||
DNN_keras[i][j] <span style="color: #666666">=</span> DNN
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Learning rate = "</span>, eta)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Test accuracy: </span><span style="color: #BB6688; font-weight: bold">%.3f</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> scores[<span style="color: #666666">1</span>])
|
||||
<span style="color: #008000; font-weight: bold">print</span>()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># optional</span>
|
||||
<span style="color: #408080; font-style: italic"># visual representation of grid search</span>
|
||||
<span style="color: #408080; font-style: italic"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">seaborn</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sns</span>
|
||||
|
||||
sns<span style="color: #666666">.</span>set()
|
||||
|
||||
train_accuracy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)))
|
||||
test_accuracy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(eta_vals)):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(lmbd_vals)):
|
||||
DNN <span style="color: #666666">=</span> DNN_keras[i][j]
|
||||
|
||||
train_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>evaluate(X_train, Y_train)[<span style="color: #666666">1</span>]
|
||||
test_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>evaluate(X_test, Y_test)[<span style="color: #666666">1</span>]
|
||||
|
||||
|
||||
fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(figsize <span style="color: #666666">=</span> (<span style="color: #666666">10</span>, <span style="color: #666666">10</span>))
|
||||
sns<span style="color: #666666">.</span>heatmap(train_accuracy, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>, ax<span style="color: #666666">=</span>ax, cmap<span style="color: #666666">=</span><span style="color: #BA2121">"viridis"</span>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Training Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(figsize <span style="color: #666666">=</span> (<span style="color: #666666">10</span>, <span style="color: #666666">10</span>))
|
||||
sns<span style="color: #666666">.</span>heatmap(test_accuracy, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>, ax<span style="color: #666666">=</span>ax, cmap<span style="color: #666666">=</span><span style="color: #BA2121">"viridis"</span>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Test Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -2447,7 +2447,546 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## And then with Tensorflow"
|
||||
"## Building neural networks in Tensorflow and Keras\n",
|
||||
"\n",
|
||||
"Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn\n",
|
||||
"and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy\n",
|
||||
"and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer. \n",
|
||||
"\n",
|
||||
"In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite\n",
|
||||
"clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or\n",
|
||||
"NumPy arrays.\n",
|
||||
"\n",
|
||||
"## Tensorflow\n",
|
||||
"\n",
|
||||
"Tensorflow is an open source library machine learning library\n",
|
||||
"developed by the Google Brain team for internal use. It was released\n",
|
||||
"under the Apache 2.0 open source license in November 9, 2015.\n",
|
||||
"\n",
|
||||
"Tensorflow is a computational framework that allows you to construct\n",
|
||||
"machine learning models at different levels of abstraction, from\n",
|
||||
"high-level, object-oriented APIs like Keras, down to the C++ kernels\n",
|
||||
"that Tensorflow is built upon. The higher levels of abstraction are\n",
|
||||
"simpler to use, but less flexible, and our choice of implementation\n",
|
||||
"should reflect the problems we are trying to solve.\n",
|
||||
"\n",
|
||||
"[Tensorflow uses](https://www.tensorflow.org/guide/graphs) so-called graphs to represent your computation\n",
|
||||
"in terms of the dependencies between individual operations, such that you first build a Tensorflow *graph*\n",
|
||||
"to represent your model, and then create a Tensorflow *session* to run the graph.\n",
|
||||
"\n",
|
||||
"In this guide we will analyze the same data as we did in our NumPy and\n",
|
||||
"scikit-learn tutorial, gathered from the MNIST database of images. We\n",
|
||||
"will give an introduction to the lower level Python Application\n",
|
||||
"Program Interfaces (APIs), and see how we use them to build our graph.\n",
|
||||
"Then we will build (effectively) the same graph in Keras, to see just\n",
|
||||
"how simple solving a machine learning problem can be.\n",
|
||||
"\n",
|
||||
"To install tensorflow on Unix/Linux systems, use pip as"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 11,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"pip3 install tensorflow"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"and/or if you use **anaconda**, just write (or install from the graphical user interface)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"conda install tensorflow"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Collect and pre-process data"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 13,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# import necessary packages\n",
|
||||
"import numpy as np\n",
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"from sklearn import datasets\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"# ensure the same random numbers appear every time\n",
|
||||
"np.random.seed(0)\n",
|
||||
"\n",
|
||||
"# display images in notebook\n",
|
||||
"%matplotlib inline\n",
|
||||
"plt.rcParams['figure.figsize'] = (12,12)\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"# download MNIST dataset\n",
|
||||
"digits = datasets.load_digits()\n",
|
||||
"\n",
|
||||
"# define inputs and labels\n",
|
||||
"inputs = digits.images\n",
|
||||
"labels = digits.target\n",
|
||||
"\n",
|
||||
"print(\"inputs = (n_inputs, pixel_width, pixel_height) = \" + str(inputs.shape))\n",
|
||||
"print(\"labels = (n_inputs) = \" + str(labels.shape))\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"# flatten the image\n",
|
||||
"# the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64\n",
|
||||
"n_inputs = len(inputs)\n",
|
||||
"inputs = inputs.reshape(n_inputs, -1)\n",
|
||||
"print(\"X = (n_inputs, n_features) = \" + str(inputs.shape))\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"# choose some random images to display\n",
|
||||
"indices = np.arange(n_inputs)\n",
|
||||
"random_indices = np.random.choice(indices, size=5)\n",
|
||||
"\n",
|
||||
"for i, image in enumerate(digits.images[random_indices]):\n",
|
||||
" plt.subplot(1, 5, i+1)\n",
|
||||
" plt.axis('off')\n",
|
||||
" plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n",
|
||||
" plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 14,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from keras.utils import to_categorical\n",
|
||||
"from sklearn.model_selection import train_test_split\n",
|
||||
"\n",
|
||||
"# one-hot representation of labels\n",
|
||||
"labels = to_categorical(labels)\n",
|
||||
"\n",
|
||||
"# split into train and test data\n",
|
||||
"train_size = 0.8\n",
|
||||
"test_size = 1 - train_size\n",
|
||||
"X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n",
|
||||
" test_size=test_size)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Using TensorFlow backend\n",
|
||||
"\n",
|
||||
"1. Define model and architecture\n",
|
||||
"\n",
|
||||
"2. Choose cost function and optimizer"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 15,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import tensorflow as tf\n",
|
||||
"\n",
|
||||
"class NeuralNetworkTensorflow:\n",
|
||||
" def __init__(\n",
|
||||
" self,\n",
|
||||
" X_train,\n",
|
||||
" Y_train,\n",
|
||||
" X_test,\n",
|
||||
" Y_test,\n",
|
||||
" n_neurons_layer1=100,\n",
|
||||
" n_neurons_layer2=50,\n",
|
||||
" n_categories=2,\n",
|
||||
" epochs=10,\n",
|
||||
" batch_size=100,\n",
|
||||
" eta=0.1,\n",
|
||||
" lmbd=0.0,\n",
|
||||
" ):\n",
|
||||
" \n",
|
||||
" # keep track of number of steps\n",
|
||||
" self.global_step = tf.Variable(0, dtype=tf.int32, trainable=False, name='global_step')\n",
|
||||
" \n",
|
||||
" self.X_train = X_train\n",
|
||||
" self.Y_train = Y_train\n",
|
||||
" self.X_test = X_test\n",
|
||||
" self.Y_test = Y_test\n",
|
||||
" \n",
|
||||
" self.n_inputs = X_train.shape[0]\n",
|
||||
" self.n_features = X_train.shape[1]\n",
|
||||
" self.n_neurons_layer1 = n_neurons_layer1\n",
|
||||
" self.n_neurons_layer2 = n_neurons_layer2\n",
|
||||
" self.n_categories = n_categories\n",
|
||||
" \n",
|
||||
" self.epochs = epochs\n",
|
||||
" self.batch_size = batch_size\n",
|
||||
" self.iterations = self.n_inputs // self.batch_size\n",
|
||||
" self.eta = eta\n",
|
||||
" self.lmbd = lmbd\n",
|
||||
" \n",
|
||||
" # build network piece by piece\n",
|
||||
" # name scopes (with) are used to enforce creation of new variables\n",
|
||||
" # https://www.tensorflow.org/guide/variables\n",
|
||||
" self.create_placeholders()\n",
|
||||
" self.create_DNN()\n",
|
||||
" self.create_loss()\n",
|
||||
" self.create_optimiser()\n",
|
||||
" self.create_accuracy()\n",
|
||||
" \n",
|
||||
" def create_placeholders(self):\n",
|
||||
" # placeholders are fine here, but \"Datasets\" are the preferred method\n",
|
||||
" # of streaming data into a model\n",
|
||||
" with tf.name_scope('data'):\n",
|
||||
" self.X = tf.placeholder(tf.float32, shape=(None, self.n_features), name='X_data')\n",
|
||||
" self.Y = tf.placeholder(tf.float32, shape=(None, self.n_categories), name='Y_data')\n",
|
||||
" \n",
|
||||
" def create_DNN(self):\n",
|
||||
" with tf.name_scope('DNN'):\n",
|
||||
" # the weights are stored to calculate regularization loss later\n",
|
||||
" \n",
|
||||
" # Fully connected layer 1\n",
|
||||
" self.W_fc1 = self.weight_variable([self.n_features, self.n_neurons_layer1], name='fc1', dtype=tf.float32)\n",
|
||||
" b_fc1 = self.bias_variable([self.n_neurons_layer1], name='fc1', dtype=tf.float32)\n",
|
||||
" a_fc1 = tf.nn.sigmoid(tf.matmul(self.X, self.W_fc1) + b_fc1)\n",
|
||||
" \n",
|
||||
" # Fully connected layer 2\n",
|
||||
" self.W_fc2 = self.weight_variable([self.n_neurons_layer1, self.n_neurons_layer2], name='fc2', dtype=tf.float32)\n",
|
||||
" b_fc2 = self.bias_variable([self.n_neurons_layer2], name='fc2', dtype=tf.float32)\n",
|
||||
" a_fc2 = tf.nn.sigmoid(tf.matmul(a_fc1, self.W_fc2) + b_fc2)\n",
|
||||
" \n",
|
||||
" # Output layer\n",
|
||||
" self.W_out = self.weight_variable([self.n_neurons_layer2, self.n_categories], name='out', dtype=tf.float32)\n",
|
||||
" b_out = self.bias_variable([self.n_categories], name='out', dtype=tf.float32)\n",
|
||||
" self.z_out = tf.matmul(a_fc2, self.W_out) + b_out\n",
|
||||
" \n",
|
||||
" def create_loss(self):\n",
|
||||
" with tf.name_scope('loss'):\n",
|
||||
" softmax_loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits_v2(labels=self.Y, logits=self.z_out))\n",
|
||||
" \n",
|
||||
" regularizer_loss_fc1 = tf.nn.l2_loss(self.W_fc1)\n",
|
||||
" regularizer_loss_fc2 = tf.nn.l2_loss(self.W_fc2)\n",
|
||||
" regularizer_loss_out = tf.nn.l2_loss(self.W_out)\n",
|
||||
" regularizer_loss = self.lmbd*(regularizer_loss_fc1 + regularizer_loss_fc2 + regularizer_loss_out)\n",
|
||||
" \n",
|
||||
" self.loss = softmax_loss + regularizer_loss\n",
|
||||
"\n",
|
||||
" def create_accuracy(self):\n",
|
||||
" with tf.name_scope('accuracy'):\n",
|
||||
" probabilities = tf.nn.softmax(self.z_out)\n",
|
||||
" predictions = tf.argmax(probabilities, axis=1)\n",
|
||||
" labels = tf.argmax(self.Y, axis=1)\n",
|
||||
" \n",
|
||||
" correct_predictions = tf.equal(predictions, labels)\n",
|
||||
" correct_predictions = tf.cast(correct_predictions, tf.float32)\n",
|
||||
" self.accuracy = tf.reduce_mean(correct_predictions)\n",
|
||||
" \n",
|
||||
" def create_optimiser(self):\n",
|
||||
" with tf.name_scope('optimizer'):\n",
|
||||
" self.optimizer = tf.train.GradientDescentOptimizer(learning_rate=self.eta).minimize(self.loss, global_step=self.global_step)\n",
|
||||
" \n",
|
||||
" def weight_variable(self, shape, name='', dtype=tf.float32):\n",
|
||||
" initial = tf.truncated_normal(shape, stddev=0.1)\n",
|
||||
" return tf.Variable(initial, name=name, dtype=dtype)\n",
|
||||
" \n",
|
||||
" def bias_variable(self, shape, name='', dtype=tf.float32):\n",
|
||||
" initial = tf.constant(0.1, shape=shape)\n",
|
||||
" return tf.Variable(initial, name=name, dtype=dtype)\n",
|
||||
" \n",
|
||||
" def fit(self):\n",
|
||||
" data_indices = np.arange(self.n_inputs)\n",
|
||||
"\n",
|
||||
" with tf.Session() as sess:\n",
|
||||
" sess.run(tf.global_variables_initializer())\n",
|
||||
" for i in range(self.epochs):\n",
|
||||
" for j in range(self.iterations):\n",
|
||||
" chosen_datapoints = np.random.choice(data_indices, size=self.batch_size, replace=False)\n",
|
||||
" batch_X, batch_Y = self.X_train[chosen_datapoints], self.Y_train[chosen_datapoints]\n",
|
||||
" \n",
|
||||
" sess.run([DNN.loss, DNN.optimizer],\n",
|
||||
" feed_dict={DNN.X: batch_X,\n",
|
||||
" DNN.Y: batch_Y})\n",
|
||||
" accuracy = sess.run(DNN.accuracy,\n",
|
||||
" feed_dict={DNN.X: batch_X,\n",
|
||||
" DNN.Y: batch_Y})\n",
|
||||
" step = sess.run(DNN.global_step)\n",
|
||||
" \n",
|
||||
" self.train_loss, self.train_accuracy = sess.run([DNN.loss, DNN.accuracy],\n",
|
||||
" feed_dict={DNN.X: self.X_train,\n",
|
||||
" DNN.Y: self.Y_train})\n",
|
||||
" \n",
|
||||
" self.test_loss, self.test_accuracy = sess.run([DNN.loss, DNN.accuracy],\n",
|
||||
" feed_dict={DNN.X: self.X_test,\n",
|
||||
" DNN.Y: self.Y_test})"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Optimizing and using gradient descent"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 16,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"epochs = 100\n",
|
||||
"batch_size = 100\n",
|
||||
"n_neurons_layer1 = 100\n",
|
||||
"n_neurons_layer2 = 50\n",
|
||||
"n_categories = 10\n",
|
||||
"\n",
|
||||
"eta_vals = np.logspace(-5, 1, 7)\n",
|
||||
"lmbd_vals = np.logspace(-5, 1, 7)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 17,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"DNN_tf = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
|
||||
" \n",
|
||||
"for i, eta in enumerate(eta_vals):\n",
|
||||
" for j, lmbd in enumerate(lmbd_vals):\n",
|
||||
" DNN = NeuralNetworkTensorflow(X_train, Y_train, X_test, Y_test,\n",
|
||||
" n_neurons_layer1, n_neurons_layer2, n_categories,\n",
|
||||
" epochs=epochs, batch_size=batch_size, eta=eta, lmbd=lmbd)\n",
|
||||
" DNN.fit()\n",
|
||||
" \n",
|
||||
" DNN_tf[i][j] = DNN\n",
|
||||
" \n",
|
||||
" print(\"Learning rate = \", eta)\n",
|
||||
" print(\"Lambda = \", lmbd)\n",
|
||||
" print(\"Test accuracy: %.3f\" % DNN.test_accuracy)\n",
|
||||
" print()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 18,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# optional\n",
|
||||
"# visual representation of grid search\n",
|
||||
"# uses seaborn heatmap, could probably do this in matplotlib\n",
|
||||
"import seaborn as sns\n",
|
||||
"\n",
|
||||
"sns.set()\n",
|
||||
"\n",
|
||||
"train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
|
||||
"test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
|
||||
"\n",
|
||||
"for i in range(len(eta_vals)):\n",
|
||||
" for j in range(len(lmbd_vals)):\n",
|
||||
" DNN = DNN_tf[i][j]\n",
|
||||
"\n",
|
||||
" train_accuracy[i][j] = DNN.train_accuracy\n",
|
||||
" test_accuracy[i][j] = DNN.test_accuracy\n",
|
||||
"\n",
|
||||
" \n",
|
||||
"fig, ax = plt.subplots(figsize = (10, 10))\n",
|
||||
"sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
|
||||
"ax.set_title(\"Training Accuracy\")\n",
|
||||
"ax.set_ylabel(\"$\\eta$\")\n",
|
||||
"ax.set_xlabel(\"$\\lambda$\")\n",
|
||||
"plt.show()\n",
|
||||
"\n",
|
||||
"fig, ax = plt.subplots(figsize = (10, 10))\n",
|
||||
"sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
|
||||
"ax.set_title(\"Test Accuracy\")\n",
|
||||
"ax.set_ylabel(\"$\\eta$\")\n",
|
||||
"ax.set_xlabel(\"$\\lambda$\")\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 19,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# optional\n",
|
||||
"# we can use log files to visualize our graph in Tensorboard\n",
|
||||
"writer = tf.summary.FileWriter('logs/')\n",
|
||||
"writer.add_graph(tf.get_default_graph())"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Using Keras\n",
|
||||
"\n",
|
||||
"Keras is a high level [neural network](https://en.wikipedia.org/wiki/Application_programming_interface)\n",
|
||||
"that supports Tensorflow, CTNK and Theano as backends. \n",
|
||||
"If you have Tensorflow installed Keras is available through the *tf.keras* module. \n",
|
||||
"If you have Anaconda installed you may run the following command"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 20,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"conda install keras"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Alternatively, if you have Tensorflow or one of the other supported backends install you may use the pip package manager:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 21,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"pip3 install keras"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"or look up the [instructions here](https://keras.io/)."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 22,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from keras.models import Sequential\n",
|
||||
"from keras.layers import Dense\n",
|
||||
"from keras.regularizers import l2\n",
|
||||
"from keras.optimizers import SGD\n",
|
||||
"\n",
|
||||
"def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):\n",
|
||||
" model = Sequential()\n",
|
||||
" model.add(Dense(n_neurons_layer1, activation='sigmoid', kernel_regularizer=l2(lmbd)))\n",
|
||||
" model.add(Dense(n_neurons_layer2, activation='sigmoid', kernel_regularizer=l2(lmbd)))\n",
|
||||
" model.add(Dense(n_categories, activation='softmax'))\n",
|
||||
" \n",
|
||||
" sgd = SGD(lr=eta)\n",
|
||||
" model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n",
|
||||
" \n",
|
||||
" return model"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 23,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n",
|
||||
" \n",
|
||||
"for i, eta in enumerate(eta_vals):\n",
|
||||
" for j, lmbd in enumerate(lmbd_vals):\n",
|
||||
" DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,\n",
|
||||
" eta=eta, lmbd=lmbd)\n",
|
||||
" DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)\n",
|
||||
" scores = DNN.evaluate(X_test, Y_test)\n",
|
||||
" \n",
|
||||
" DNN_keras[i][j] = DNN\n",
|
||||
" \n",
|
||||
" print(\"Learning rate = \", eta)\n",
|
||||
" print(\"Lambda = \", lmbd)\n",
|
||||
" print(\"Test accuracy: %.3f\" % scores[1])\n",
|
||||
" print()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 24,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# optional\n",
|
||||
"# visual representation of grid search\n",
|
||||
"# uses seaborn heatmap, could probably do this in matplotlib\n",
|
||||
"import seaborn as sns\n",
|
||||
"\n",
|
||||
"sns.set()\n",
|
||||
"\n",
|
||||
"train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
|
||||
"test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n",
|
||||
"\n",
|
||||
"for i in range(len(eta_vals)):\n",
|
||||
" for j in range(len(lmbd_vals)):\n",
|
||||
" DNN = DNN_keras[i][j]\n",
|
||||
"\n",
|
||||
" train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[1]\n",
|
||||
" test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[1]\n",
|
||||
"\n",
|
||||
" \n",
|
||||
"fig, ax = plt.subplots(figsize = (10, 10))\n",
|
||||
"sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
|
||||
"ax.set_title(\"Training Accuracy\")\n",
|
||||
"ax.set_ylabel(\"$\\eta$\")\n",
|
||||
"ax.set_xlabel(\"$\\lambda$\")\n",
|
||||
"plt.show()\n",
|
||||
"\n",
|
||||
"fig, ax = plt.subplots(figsize = (10, 10))\n",
|
||||
"sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n",
|
||||
"ax.set_title(\"Test Accuracy\")\n",
|
||||
"ax.set_ylabel(\"$\\eta$\")\n",
|
||||
"ax.set_xlabel(\"$\\lambda$\")\n",
|
||||
"plt.show()"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
||||
Binary file not shown.
Binary file not shown.
@@ -1824,7 +1824,7 @@ conda install tensorflow
|
||||
!split
|
||||
===== Collect and pre-process data =====
|
||||
|
||||
bc pycod
|
||||
!bc pycod
|
||||
# import necessary packages
|
||||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
|
||||
Reference in New Issue
Block a user