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="._NeuralNet-bs047.html#___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="#___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="._NeuralNet-bs047.html#___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>
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<!-- navigation toc: --> <li><a href="#___sec53" 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-bs055.html#___sec54" style="font-size: 80%;"><b>Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs056.html#___sec55" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
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<!-- 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>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs059.html#___sec58" style="font-size: 80%;"><b>Using Keras</b></a></li>
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<!-- 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>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs063.html#___sec62" style="font-size: 80%;"><b>The RELU function family</b></a></li>
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<!-- 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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@@ -257,48 +259,18 @@ MathJax.Hub.Config({
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<a name="part0054"></a>
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<!-- !split -->
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<h2 id="___sec53" class="anchor">Tensorflow </h2>
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<h2 id="___sec53" class="anchor">Building neural networks in Tensorflow and Keras </h2>
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<p>
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Tensorflow is an open source library machine learning library
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developed by the Google Brain team for internal use. It was released
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under the Apache 2.0 open source license in November 9, 2015.
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Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn
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and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
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and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.
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<p>
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Tensorflow is a computational framework that allows you to construct
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machine learning models at different levels of abstraction, from
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high-level, object-oriented APIs like Keras, down to the C++ kernels
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that Tensorflow is built upon. The higher levels of abstraction are
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simpler to use, but less flexible, and our choice of implementation
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should reflect the problems we are trying to solve.
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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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clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or
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NumPy arrays.
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<p>
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<a href="https://www.tensorflow.org/guide/graphs" target="_self">Tensorflow uses</a> so-called graphs to represent your computation
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in terms of the dependencies between individual operations, such that you first build a Tensorflow <em>graph</em>
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to represent your model, and then create a Tensorflow <em>session</em> to run the graph.
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<p>
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In this guide we will analyze the same data as we did in our NumPy and
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scikit-learn tutorial, gathered from the MNIST database of images. We
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will give an introduction to the lower level Python Application
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Program Interfaces (APIs), and see how we use them to build our graph.
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Then we will build (effectively) the same graph in Keras, to see just
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how simple solving a machine learning problem can be.
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<p>
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To install tensorflow on Unix/Linux systems, use pip as
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<p>
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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>pip3 install tensorflow
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</pre></div>
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<p>
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and/or if you use <b>anaconda</b>, just write (or install from the graphical user interface)
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<p>
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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>conda install tensorflow
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</pre></div>
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<p>
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<p>
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<!-- navigation buttons at the bottom of the page -->
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@@ -325,7 +297,7 @@ and/or if you use <b>anaconda</b>, just write (or install from the graphical use
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<li><a href="._NeuralNet-bs062.html">63</a></li>
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<li><a href="._NeuralNet-bs063.html">64</a></li>
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<li><a href="">...</a></li>
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<li><a href="._NeuralNet-bs065.html">66</a></li>
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<li><a href="._NeuralNet-bs066.html">67</a></li>
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<li><a href="._NeuralNet-bs055.html">»</a></li>
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</ul>
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