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="._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="#___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="._NeuralNet-bs054.html#___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="#___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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@@ -255,46 +257,24 @@ MathJax.Hub.Config({
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0064"></a>
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<!-- !split -->
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<!-- !split -->
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<h2 id="___sec63" class="anchor">A top-down perspective on Neural networks </h2>
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<h2 id="___sec63" class="anchor">Which activation function should we use? </h2>
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<p>
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The first thing we would like to do is divide the data into two or three
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parts. A training set, a validation or dev (development) set, and a
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test set. The test set is the data on which we want to make
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predictions. The dev set is a subset of the training data we use to
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check how well we are doing out-of-sample, after training the model on
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the training dataset. We use the validation error as a proxy for the
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test error in order to make tweaks to our model. It is crucial that we
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do not use any of the test data to train the algorithm. This is a
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cardinal sin in ML. Then:
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<ul>
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<li> Estimate optimal error rate</li>
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<li> Minimize underfitting (bias) on training data set.</li>
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<li> Make sure you are not overfitting.</li>
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</ul>
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If the validation and test sets are drawn from the same distributions,
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then a good performance on the validation set should lead to similarly
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good performance on the test set.
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In general it seems that the ELU activation function is better than
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the leaky ReLU function (and its variants), which is better than
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ReLU. ReLU performs better than \( \tanh \) which in turn performs better
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than the logistic function.
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<p>
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However, sometimes
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the training data and test data differ in subtle ways because, for
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example, they are collected using slightly different methods, or
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because it is cheaper to collect data in one way versus another. In
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this case, there can be a mismatch between the training and test
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data. This can lead to the neural network overfitting these small
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differences between the test and training sets, and a poor performance
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on the test set despite having a good performance on the validation
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set. To rectify this, Andrew Ng suggests making two validation or dev
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sets, one constructed from the training data and one constructed from
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the test data. The difference between the performance of the algorithm
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on these two validation sets quantifies the train-test mismatch. This
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can serve as another important diagnostic when using DNNs for
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supervised learning.
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If runtime
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performance is an issue, then you may opt for the leaky ReLU function over the
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ELU function If you don’t
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want to tweak yet another hyperparameter, you may just use the default
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\( \alpha \) of \( 0.01 \) for the leaky ReLU, and \( 1 \) for ELU. If you have
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spare time and computing power, you can use cross-validation or
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bootstrap to evaluate other activation functions.
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<p>
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<p>
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@@ -313,6 +293,7 @@ supervised learning.
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<li><a href="._NeuralNet-bs063.html">64</a></li>
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<li class="active"><a href="._NeuralNet-bs064.html">65</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-bs065.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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