mhjensen
457 lines
31 KiB
HTML
457 lines
31 KiB
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{'highest level': 2,
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'sections': [('Neural networks', 2, None, '___sec0'),
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('Artificial neurons', 2, None, '___sec1'),
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('Neural network types', 2, None, '___sec2'),
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('Feed-forward neural networks', 2, None, '___sec3'),
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('Developing a code for doing neural networks with back '
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('Define model and architecture', 2, None, '___sec37'),
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('Weights and biases', 2, None, '___sec39'),
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('Feed-forward pass', 2, None, '___sec40'),
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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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('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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('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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'___sec64'),
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('Limitations of supervised learning with deep networks',
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('Convolutional Neural Networks (recognizing images)',
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('Regular NNs don’t scale well to full images',
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('The MNIST dataset again', 2, None, '___sec74'),
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('Reformulating the problem', 2, None, '___sec90'),
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('Estimating errors', 2, None, '___sec91'),
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('Creating a simple Deep Neural Net', 2, None, '___sec92'),
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('Setting up the code, feed forward part', 2, None, '___sec93'),
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('And adding Back propagation', 2, None, '___sec99'),
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('Using a deep neural network', 2, None, '___sec102'),
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('Wrapping it up', 2, None, '___sec103')]}
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end of tocinfo -->
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<a class="navbar-brand" href="NeuralNet-bs.html">Data Analysis and Machine Learning: Neural networks, from the simple perceptron to deep learning and convolutional networks</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs001.html#___sec0" style="font-size: 80%;"><b>Neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs002.html#___sec1" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs003.html#___sec2" style="font-size: 80%;"><b>Neural network types</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs004.html#___sec3" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs005.html#___sec4" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs006.html#___sec5" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs007.html#___sec6" style="font-size: 80%;"><b>Other types of networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs008.html#___sec7" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs009.html#___sec8" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs010.html#___sec9" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs011.html#___sec10" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs012.html#___sec11" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs013.html#___sec12" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs014.html#___sec13" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs015.html#___sec14" style="font-size: 80%;"> Matrix-vector notation</a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs016.html#___sec15" style="font-size: 80%;"> Matrix-vector notation and activation</a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs017.html#___sec16" style="font-size: 80%;"> Activation functions</a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs018.html#___sec17" style="font-size: 80%;"> Activation functions, Logistic and Hyperbolic ones</a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs019.html#___sec18" style="font-size: 80%;"> Relevance</a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs020.html#___sec19" style="font-size: 80%;"><b>The multilayer perceptron (MLP)</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs021.html#___sec20" style="font-size: 80%;"><b>From one to many layers, the universal approximation theorem</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs022.html#___sec21" style="font-size: 80%;"><b>Deriving the back propagation code for a multilayer perceptron model</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs023.html#___sec22" style="font-size: 80%;"><b>Definitions</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs024.html#___sec23" style="font-size: 80%;"><b>Derivatives and the chain rule</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs025.html#___sec24" style="font-size: 80%;"><b>Derivative of the cost function</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs026.html#___sec25" style="font-size: 80%;"><b>Bringing it together, first back propagation equation</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs027.html#___sec26" style="font-size: 80%;"><b>Derivatives in terms of \( z_j^L \)</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs028.html#___sec27" style="font-size: 80%;"><b>Bringing it together</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs029.html#___sec28" style="font-size: 80%;"><b>Final back propagating equation</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs030.html#___sec29" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
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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>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="#___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>
|
||
<!-- 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>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs042.html#___sec41" style="font-size: 80%;"><b>Matrix multiplications</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs043.html#___sec42" style="font-size: 80%;"><b>Choose cost function and optimizer</b></a></li>
|
||
<!-- 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>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Improving performance</b></a></li>
|
||
<!-- 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>
|
||
<!-- 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>
|
||
<!-- 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>
|
||
<!-- 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>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs065.html#___sec64" style="font-size: 80%;"><b>A top-down perspective on Neural networks</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs066.html#___sec65" style="font-size: 80%;"><b>Limitations of supervised learning with deep networks</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs067.html#___sec66" style="font-size: 80%;"><b>Convolutional Neural Networks (recognizing images)</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs068.html#___sec67" style="font-size: 80%;"><b>Regular NNs don’t scale well to full images</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs069.html#___sec68" style="font-size: 80%;"><b>3D volumes of neurons</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs070.html#___sec69" style="font-size: 80%;"><b>Layers used to build CNNs</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs071.html#___sec70" style="font-size: 80%;"><b>Transforming images</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs072.html#___sec71" style="font-size: 80%;"><b>CNNs in brief</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs073.html#___sec72" style="font-size: 80%;"><b>CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs074.html#___sec73" style="font-size: 80%;"><b>Setting it up</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs075.html#___sec74" style="font-size: 80%;"><b>The MNIST dataset again</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs076.html#___sec75" style="font-size: 80%;"><b>Strong correlations</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs077.html#___sec76" style="font-size: 80%;"><b>Layers of a CNN</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs078.html#___sec77" style="font-size: 80%;"><b>Systematic reduction</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs079.html#___sec78" style="font-size: 80%;"><b>Prerequisites: Collect and pre-process data</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs080.html#___sec79" style="font-size: 80%;"><b>Importing Keras and Tensorflow</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs081.html#___sec80" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs082.html#___sec81" style="font-size: 80%;"><b>Train the model</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs083.html#___sec82" style="font-size: 80%;"><b>Visualizing the results</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs084.html#___sec83" style="font-size: 80%;"><b>Running with Keras</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs085.html#___sec84" style="font-size: 80%;"><b>Final part</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs086.html#___sec85" style="font-size: 80%;"><b>Final visualization</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs087.html#___sec86" style="font-size: 80%;"><b>Fun links</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs088.html#___sec87" style="font-size: 80%;"><b>Applications: solving ordinary differential equations with Neural Networks</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs089.html#___sec88" style="font-size: 80%;"><b>Trial solution</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs090.html#___sec89" style="font-size: 80%;"><b>More details</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs091.html#___sec90" style="font-size: 80%;"><b>Reformulating the problem</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs092.html#___sec91" style="font-size: 80%;"><b>Estimating errors</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs093.html#___sec92" style="font-size: 80%;"><b>Creating a simple Deep Neural Net</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs094.html#___sec93" style="font-size: 80%;"><b>Setting up the code, feed forward part</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs095.html#___sec94" style="font-size: 80%;"><b>Backpropagation</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs096.html#___sec95" style="font-size: 80%;"><b>Gradient Descent</b></a></li>
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||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs097.html#___sec96" style="font-size: 80%;"><b>More on GD and cost function</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs098.html#___sec97" style="font-size: 80%;"><b>An implementation of a Deep Neural Network</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs099.html#___sec98" style="font-size: 80%;"><b>The final parts of the code</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs100.html#___sec99" style="font-size: 80%;"><b>And adding Back propagation</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs101.html#___sec100" style="font-size: 80%;"><b>Solving the ODE</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs102.html#___sec101" style="font-size: 80%;"><b>Using neural network</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs103.html#___sec102" style="font-size: 80%;"><b>Using a deep neural network</b></a></li>
|
||
<!-- navigation toc: --> <li><a href="._NeuralNet-bs104.html#___sec103" style="font-size: 80%;"><b>Wrapping it up</b></a></li>
|
||
|
||
</ul>
|
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</li>
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||
</ul>
|
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<div class="container">
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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|
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<a name="part0037"></a>
|
||
<!-- !split -->
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|
||
<h2 id="___sec36" class="anchor">Train and test datasets </h2>
|
||
|
||
<p>
|
||
Performing analysis before partitioning the dataset is a major error, that can lead to incorrect conclusions.
|
||
|
||
<p>
|
||
We will reserve \( 80 \% \) of our dataset for training and \( 20 \% \) for testing.
|
||
|
||
<p>
|
||
It is important that the train and test datasets are drawn randomly from our dataset, to ensure
|
||
no bias in the sampling.
|
||
Say you are taking measurements of weather data to predict the weather in the coming 5 days.
|
||
You don't want to train your model on measurements taken from the hours 00.00 to 12.00, and then test it on data
|
||
collected from 12.00 to 24.00.
|
||
|
||
<p>
|
||
|
||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
|
||
|
||
<span style="color: #408080; font-style: italic"># one-liner from scikit-learn library</span>
|
||
train_size <span style="color: #666666">=</span> <span style="color: #666666">0.8</span>
|
||
test_size <span style="color: #666666">=</span> <span style="color: #666666">1</span> <span style="color: #666666">-</span> train_size
|
||
X_train, X_test, Y_train, Y_test <span style="color: #666666">=</span> train_test_split(inputs, labels, train_size<span style="color: #666666">=</span>train_size,
|
||
test_size<span style="color: #666666">=</span>test_size)
|
||
|
||
<span style="color: #408080; font-style: italic"># equivalently in numpy</span>
|
||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">train_test_split_numpy</span>(inputs, labels, train_size, test_size):
|
||
n_inputs <span style="color: #666666">=</span> <span style="color: #008000">len</span>(inputs)
|
||
inputs_shuffled <span style="color: #666666">=</span> inputs<span style="color: #666666">.</span>copy()
|
||
labels_shuffled <span style="color: #666666">=</span> labels<span style="color: #666666">.</span>copy()
|
||
|
||
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>shuffle(inputs_shuffled)
|
||
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>shuffle(labels_shuffled)
|
||
|
||
train_end <span style="color: #666666">=</span> <span style="color: #008000">int</span>(n_inputs<span style="color: #666666">*</span>train_size)
|
||
X_train, X_test <span style="color: #666666">=</span> inputs_shuffled[:train_end], inputs_shuffled[train_end:]
|
||
Y_train, Y_test <span style="color: #666666">=</span> labels_shuffled[:train_end], labels_shuffled[train_end:]
|
||
|
||
<span style="color: #008000; font-weight: bold">return</span> X_train, X_test, Y_train, Y_test
|
||
|
||
<span style="color: #408080; font-style: italic">#X_train, X_test, Y_train, Y_test = train_test_split_numpy(inputs, labels, train_size, test_size)</span>
|
||
|
||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Number of training images: "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(<span style="color: #008000">len</span>(X_train)))
|
||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Number of test images: "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(<span style="color: #008000">len</span>(X_test)))
|
||
</pre></div>
|
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<p>
|
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