small update on neural networks
This commit is contained in:
mhjensen
@@ -92,54 +92,55 @@ Automatically generated HTML file from DocOnce source
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'___sec30'),
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('Defining the cost function', 2, None, '___sec31'),
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('Example: binary classification problem', 2, None, '___sec32'),
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('The Softmax function', 2, None, '___sec33'),
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('Developing a code for doing neural networks with back '
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'propagation',
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2,
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None,
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'___sec33'),
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('Collect and pre-process data', 2, None, '___sec34'),
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('Train and test datasets', 2, None, '___sec35'),
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('Define model and architecture', 2, None, '___sec36'),
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('Layers', 2, None, '___sec37'),
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('Weights and biases', 2, None, '___sec38'),
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('Feed-forward pass', 2, None, '___sec39'),
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('Matrix multiplications', 2, None, '___sec40'),
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('Choose cost function and optimizer', 2, None, '___sec41'),
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('Optimizing the cost function', 2, None, '___sec42'),
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('Regularization', 2, None, '___sec43'),
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('Matrix multiplication', 2, None, '___sec44'),
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('Improving performance', 2, None, '___sec45'),
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('Full object-oriented implementation', 2, None, '___sec46'),
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('Evaluate model performance on test data', 2, None, '___sec47'),
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('Adjust hyperparameters', 2, None, '___sec48'),
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('Visualization', 2, None, '___sec49'),
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('scikit-learn implementation', 2, None, '___sec50'),
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('Visualization', 2, None, '___sec51'),
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'___sec34'),
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('Collect and pre-process data', 2, None, '___sec35'),
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('Train and test datasets', 2, None, '___sec36'),
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('Define model and architecture', 2, None, '___sec37'),
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('Layers', 2, None, '___sec38'),
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('Weights and biases', 2, None, '___sec39'),
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('Feed-forward pass', 2, None, '___sec40'),
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('Matrix multiplications', 2, None, '___sec41'),
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('Choose cost function and optimizer', 2, None, '___sec42'),
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('Optimizing the cost function', 2, None, '___sec43'),
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('Regularization', 2, None, '___sec44'),
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('Matrix multiplication', 2, None, '___sec45'),
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('Improving performance', 2, None, '___sec46'),
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('Full object-oriented implementation', 2, None, '___sec47'),
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('Evaluate model performance on test data', 2, None, '___sec48'),
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('Adjust hyperparameters', 2, None, '___sec49'),
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('Visualization', 2, None, '___sec50'),
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('scikit-learn implementation', 2, None, '___sec51'),
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('Visualization', 2, None, '___sec52'),
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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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'___sec52'),
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('Tensorflow', 2, None, '___sec53'),
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('Collect and pre-process data', 2, None, '___sec54'),
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('Using TensorFlow backend', 2, None, '___sec55'),
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('Optimizing and using gradient descent', 2, None, '___sec56'),
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('Using Keras', 2, None, '___sec57'),
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('Which activation function should I use?', 2, None, '___sec58'),
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'___sec53'),
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('Tensorflow', 2, None, '___sec54'),
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('Collect and pre-process data', 2, None, '___sec55'),
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('Using TensorFlow backend', 2, None, '___sec56'),
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('Optimizing and using gradient descent', 2, None, '___sec57'),
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('Using Keras', 2, None, '___sec58'),
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('Which activation function should I use?', 2, None, '___sec59'),
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('Is the Logistic activation function (Sigmoid) our choice?',
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2,
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None,
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'___sec59'),
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('The derivative of the Logistic funtion', 2, None, '___sec60'),
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('The RELU function family', 2, None, '___sec61'),
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('Which activation function should we use?', 2, None, '___sec62'),
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'___sec60'),
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('The derivative of the Logistic funtion', 2, None, '___sec61'),
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('The RELU function family', 2, None, '___sec62'),
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('Which activation function should we use?', 2, None, '___sec63'),
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('A top-down perspective on Neural networks',
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2,
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None,
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'___sec63'),
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'___sec64'),
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('Limitations of supervised learning with deep networks',
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2,
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None,
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'___sec64')]}
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'___sec65')]}
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end of tocinfo -->
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<body>
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@@ -210,38 +211,39 @@ MathJax.Hub.Config({
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<!-- 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>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs032.html#___sec31" style="font-size: 80%;"><b>Defining the cost function</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs033.html#___sec32" style="font-size: 80%;"><b>Example: binary classification problem</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs034.html#___sec33" style="font-size: 80%;"><b>Developing a code for doing neural networks with back propagation</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs035.html#___sec34" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs036.html#___sec35" style="font-size: 80%;"><b>Train and test datasets</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs037.html#___sec36" style="font-size: 80%;"><b>Define model and architecture</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs038.html#___sec37" style="font-size: 80%;"><b>Layers</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs039.html#___sec38" style="font-size: 80%;"><b>Weights and biases</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs040.html#___sec39" style="font-size: 80%;"><b>Feed-forward pass</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs041.html#___sec40" style="font-size: 80%;"><b>Matrix multiplications</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs042.html#___sec41" style="font-size: 80%;"><b>Choose cost function and optimizer</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs043.html#___sec42" style="font-size: 80%;"><b>Optimizing the cost function</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs044.html#___sec43" style="font-size: 80%;"><b>Regularization</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs045.html#___sec44" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs046.html#___sec45" style="font-size: 80%;"><b>Improving performance</b></a></li>
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<!-- navigation toc: --> <li><a href="#___sec46" style="font-size: 80%;"><b>Full object-oriented implementation</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>Adjust hyperparameters</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Visualization</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Visualization</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" 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-bs054.html#___sec53" style="font-size: 80%;"><b>Tensorflow</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs056.html#___sec55" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs057.html#___sec56" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs058.html#___sec57" style="font-size: 80%;"><b>Using Keras</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs059.html#___sec58" style="font-size: 80%;"><b>Which activation function should I use?</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs060.html#___sec59" style="font-size: 80%;"><b>Is the Logistic activation function (Sigmoid) our choice?</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs061.html#___sec60" style="font-size: 80%;"><b>The derivative of the Logistic funtion</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs062.html#___sec61" style="font-size: 80%;"><b>The RELU function family</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs063.html#___sec62" style="font-size: 80%;"><b>Which activation function should we use?</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs064.html#___sec63" style="font-size: 80%;"><b>A top-down perspective on Neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs065.html#___sec64" style="font-size: 80%;"><b>Limitations of supervised learning with deep networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs034.html#___sec33" style="font-size: 80%;"><b>The Softmax function</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs035.html#___sec34" style="font-size: 80%;"><b>Developing a code for doing neural networks with back propagation</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs036.html#___sec35" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs037.html#___sec36" style="font-size: 80%;"><b>Train and test datasets</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs038.html#___sec37" style="font-size: 80%;"><b>Define model and architecture</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs039.html#___sec38" style="font-size: 80%;"><b>Layers</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs040.html#___sec39" style="font-size: 80%;"><b>Weights and biases</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs041.html#___sec40" style="font-size: 80%;"><b>Feed-forward pass</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs042.html#___sec41" style="font-size: 80%;"><b>Matrix multiplications</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs043.html#___sec42" style="font-size: 80%;"><b>Choose cost function and optimizer</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs044.html#___sec43" style="font-size: 80%;"><b>Optimizing the cost function</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs045.html#___sec44" style="font-size: 80%;"><b>Regularization</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs046.html#___sec45" style="font-size: 80%;"><b>Matrix multiplication</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="#___sec46" style="font-size: 80%;"><b>Improving performance</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs048.html#___sec47" style="font-size: 80%;"><b>Full object-oriented implementation</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>Adjust hyperparameters</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs051.html#___sec50" style="font-size: 80%;"><b>Visualization</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Visualization</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Building neural networks in Tensorflow and Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Tensorflow</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs056.html#___sec55" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs057.html#___sec56" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs058.html#___sec57" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs059.html#___sec58" style="font-size: 80%;"><b>Using Keras</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs060.html#___sec59" style="font-size: 80%;"><b>Which activation function should I use?</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs061.html#___sec60" style="font-size: 80%;"><b>Is the Logistic activation function (Sigmoid) our choice?</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs062.html#___sec61" style="font-size: 80%;"><b>The derivative of the Logistic funtion</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs063.html#___sec62" style="font-size: 80%;"><b>The RELU function family</b></a></li>
|
||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs064.html#___sec63" style="font-size: 80%;"><b>Which activation function should we use?</b></a></li>
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||||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs065.html#___sec64" style="font-size: 80%;"><b>A top-down perspective on Neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs066.html#___sec65" style="font-size: 80%;"><b>Limitations of supervised learning with deep networks</b></a></li>
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</ul>
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</li>
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@@ -257,116 +259,23 @@ MathJax.Hub.Config({
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<a name="part0047"></a>
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<!-- !split -->
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<h2 id="___sec46" class="anchor">Full object-oriented implementation </h2>
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<h2 id="___sec46" class="anchor">Improving performance </h2>
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<p>
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It is very natural to think of the network as an object, with specific instances of the network
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being realizations of this object with different hyperparameters. An implementation using Python classes provides a clean structure and interface, and the full implementation of our neural network is given below.
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As we can see the network does not seem to be learning at all. It seems to be just guessing the label for each image.
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In order to obtain a network that does something useful, we will have to do a bit more work.
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<p>
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The choice of <em>hyperparameters</em> such as learning rate and regularization parameter is hugely influential for the performance of the network. Typically a <em>grid-search</em> is performed, wherein we test different hyperparameters separated by orders of magnitude. For example we could test the learning rates \( \eta = 10^{-6}, 10^{-5},...,10^{-1} \) with different regularization parameters \( \lambda = 10^{-6},...,10^{-0} \).
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">class</span> <span style="color: #0000FF; font-weight: bold">NeuralNetwork</span>:
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">__init__</span>(
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<span style="color: #008000">self</span>,
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X_data,
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Y_data,
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n_hidden_neurons<span style="color: #666666">=50</span>,
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n_categories<span style="color: #666666">=10</span>,
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epochs<span style="color: #666666">=10</span>,
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batch_size<span style="color: #666666">=100</span>,
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eta<span style="color: #666666">=0.1</span>,
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lmbd<span style="color: #666666">=0.0</span>,
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<p>
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Next, we haven't implemented minibatching yet, which introduces stochasticity and is though to act as an important regularizer on the weights. We call a feed-forward + backward pass with a minibatch an <em>iteration</em>, and a full training period
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going through the entire dataset (\( n/M \) batches) an <em>epoch</em>.
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):
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<span style="color: #008000">self</span><span style="color: #666666">.</span>X_data_full <span style="color: #666666">=</span> X_data
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<span style="color: #008000">self</span><span style="color: #666666">.</span>Y_data_full <span style="color: #666666">=</span> Y_data
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<p>
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If this does not improve network performance, you may want to consider altering the network architecture, adding more neurons or hidden layers.
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Andrew Ng goes through some of these considerations in this <a href="https://youtu.be/F1ka6a13S9I" target="_self">video</a>. You can find a summary of the video <a href="https://kevinzakka.github.io/2016/09/26/applying-deep-learning/" target="_self">here</a>.
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<span style="color: #008000">self</span><span style="color: #666666">.</span>n_inputs <span style="color: #666666">=</span> X_data<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>]
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<span style="color: #008000">self</span><span style="color: #666666">.</span>n_features <span style="color: #666666">=</span> X_data<span style="color: #666666">.</span>shape[<span style="color: #666666">1</span>]
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<span style="color: #008000">self</span><span style="color: #666666">.</span>n_hidden_neurons <span style="color: #666666">=</span> n_hidden_neurons
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<span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories <span style="color: #666666">=</span> n_categories
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<span style="color: #008000">self</span><span style="color: #666666">.</span>epochs <span style="color: #666666">=</span> epochs
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<span style="color: #008000">self</span><span style="color: #666666">.</span>batch_size <span style="color: #666666">=</span> batch_size
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<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
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<span style="color: #008000">self</span><span style="color: #666666">.</span>eta <span style="color: #666666">=</span> eta
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<span style="color: #008000">self</span><span style="color: #666666">.</span>lmbd <span style="color: #666666">=</span> lmbd
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<span style="color: #008000">self</span><span style="color: #666666">.</span>create_biases_and_weights()
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_biases_and_weights</span>(<span style="color: #008000">self</span>):
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<span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_weights <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<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_hidden_neurons)
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<span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_bias <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(<span style="color: #008000">self</span><span style="color: #666666">.</span>n_hidden_neurons) <span style="color: #666666">+</span> <span style="color: #666666">0.01</span>
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<span style="color: #008000">self</span><span style="color: #666666">.</span>output_weights <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #008000">self</span><span style="color: #666666">.</span>n_hidden_neurons, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>output_bias <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros(<span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories) <span style="color: #666666">+</span> <span style="color: #666666">0.01</span>
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">feed_forward</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #408080; font-style: italic"># feed-forward for training</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>z_h <span style="color: #666666">=</span> np<span style="color: #666666">.</span>matmul(<span style="color: #008000">self</span><span style="color: #666666">.</span>X_data, <span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_weights) <span style="color: #666666">+</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_bias
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>a_h <span style="color: #666666">=</span> sigmoid(<span style="color: #008000">self</span><span style="color: #666666">.</span>z_h)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>z_o <span style="color: #666666">=</span> np<span style="color: #666666">.</span>matmul(<span style="color: #008000">self</span><span style="color: #666666">.</span>a_h, <span style="color: #008000">self</span><span style="color: #666666">.</span>output_weights) <span style="color: #666666">+</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>output_bias
|
||||
|
||||
exp_term <span style="color: #666666">=</span> np<span style="color: #666666">.</span>exp(<span style="color: #008000">self</span><span style="color: #666666">.</span>z_o)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>probabilities <span style="color: #666666">=</span> exp_term <span style="color: #666666">/</span> np<span style="color: #666666">.</span>sum(exp_term, axis<span style="color: #666666">=1</span>, keepdims<span style="color: #666666">=</span><span style="color: #008000">True</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">feed_forward_out</span>(<span style="color: #008000">self</span>, X):
|
||||
<span style="color: #408080; font-style: italic"># feed-forward for output</span>
|
||||
z_h <span style="color: #666666">=</span> np<span style="color: #666666">.</span>matmul(X, <span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_weights) <span style="color: #666666">+</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_bias
|
||||
a_h <span style="color: #666666">=</span> sigmoid(z_h)
|
||||
|
||||
z_o <span style="color: #666666">=</span> np<span style="color: #666666">.</span>matmul(a_h, <span style="color: #008000">self</span><span style="color: #666666">.</span>output_weights) <span style="color: #666666">+</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>output_bias
|
||||
|
||||
exp_term <span style="color: #666666">=</span> np<span style="color: #666666">.</span>exp(z_o)
|
||||
probabilities <span style="color: #666666">=</span> exp_term <span style="color: #666666">/</span> np<span style="color: #666666">.</span>sum(exp_term, axis<span style="color: #666666">=1</span>, keepdims<span style="color: #666666">=</span><span style="color: #008000">True</span>)
|
||||
<span style="color: #008000; font-weight: bold">return</span> probabilities
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">backpropagation</span>(<span style="color: #008000">self</span>):
|
||||
error_output <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>probabilities <span style="color: #666666">-</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_data
|
||||
error_hidden <span style="color: #666666">=</span> np<span style="color: #666666">.</span>matmul(error_output, <span style="color: #008000">self</span><span style="color: #666666">.</span>output_weights<span style="color: #666666">.</span>T) <span style="color: #666666">*</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>a_h <span style="color: #666666">*</span> (<span style="color: #666666">1</span> <span style="color: #666666">-</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>a_h)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>output_weights_gradient <span style="color: #666666">=</span> np<span style="color: #666666">.</span>matmul(<span style="color: #008000">self</span><span style="color: #666666">.</span>a_h<span style="color: #666666">.</span>T, error_output)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>output_bias_gradient <span style="color: #666666">=</span> np<span style="color: #666666">.</span>sum(error_output, axis<span style="color: #666666">=0</span>)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_weights_gradient <span style="color: #666666">=</span> np<span style="color: #666666">.</span>matmul(<span style="color: #008000">self</span><span style="color: #666666">.</span>X_data<span style="color: #666666">.</span>T, error_hidden)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_bias_gradient <span style="color: #666666">=</span> np<span style="color: #666666">.</span>sum(error_hidden, axis<span style="color: #666666">=0</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">if</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>lmbd <span style="color: #666666">></span> <span style="color: #666666">0.0</span>:
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>output_weights_gradient <span style="color: #666666">+=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>lmbd <span style="color: #666666">*</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>output_weights
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_weights_gradient <span style="color: #666666">+=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>lmbd <span style="color: #666666">*</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_weights
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>output_weights <span style="color: #666666">-=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>eta <span style="color: #666666">*</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>output_weights_gradient
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>output_bias <span style="color: #666666">-=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>eta <span style="color: #666666">*</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>output_bias_gradient
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_weights <span style="color: #666666">-=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>eta <span style="color: #666666">*</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_weights_gradient
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_bias <span style="color: #666666">-=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>eta <span style="color: #666666">*</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>hidden_bias_gradient
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">predict</span>(<span style="color: #008000">self</span>, X):
|
||||
probabilities <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>feed_forward_out(X)
|
||||
<span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>argmax(probabilities, axis<span style="color: #666666">=1</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">predict_probabilities</span>(<span style="color: #008000">self</span>, X):
|
||||
probabilities <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>feed_forward_out(X)
|
||||
<span style="color: #008000; font-weight: bold">return</span> probabilities
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">train</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">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):
|
||||
<span style="color: #408080; font-style: italic"># pick datapoints with replacement</span>
|
||||
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>
|
||||
)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># minibatch training data</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>X_data <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>X_data_full[chosen_datapoints]
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>Y_data <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_data_full[chosen_datapoints]
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>feed_forward()
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>backpropagation()
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
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|
||||
@@ -393,7 +302,7 @@ being realizations of this object with different hyperparameters. An implementat
|
||||
<li><a href="._NeuralNet-bs055.html">56</a></li>
|
||||
<li><a href="._NeuralNet-bs056.html">57</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._NeuralNet-bs065.html">66</a></li>
|
||||
<li><a href="._NeuralNet-bs066.html">67</a></li>
|
||||
<li><a href="._NeuralNet-bs048.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
Reference in New Issue
Block a user