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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="#___sec18" style="font-size: 80%;"><b>Setting up a Multi-layer perceptron model</b></a></li>
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<h2 id="___sec18" class="anchor">Setting up a Multi-layer perceptron model </h2>
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<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">scipy</span> <span style="color: #008000; font-weight: bold">import</span> optimize
<span style="color: #008000; font-weight: bold">class</span> <span style="color: #0000FF; font-weight: bold">Neural_Network</span>(<span style="color: #008000">object</span>):
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">__init__</span>(<span style="color: #008000">self</span>, Lambda<span style="color: #666666">=0</span>):
<span style="color: #408080; font-style: italic">#Define Hyperparameters</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>inputLayerSize <span style="color: #666666">=</span> <span style="color: #666666">2</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>outputLayerSize <span style="color: #666666">=</span> <span style="color: #666666">1</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>hiddenLayerSize <span style="color: #666666">=</span> <span style="color: #666666">3</span>
<span style="color: #408080; font-style: italic">#Weights (parameters)</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>W1 <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>inputLayerSize,<span style="color: #008000">self</span><span style="color: #666666">.</span>hiddenLayerSize)
<span style="color: #008000">self</span><span style="color: #666666">.</span>W2 <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>hiddenLayerSize,<span style="color: #008000">self</span><span style="color: #666666">.</span>outputLayerSize)
<span style="color: #408080; font-style: italic">#Regularization Parameter:</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>Lambda <span style="color: #666666">=</span> Lambda
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">forward</span>(<span style="color: #008000">self</span>, X):
<span style="color: #408080; font-style: italic">#Propogate inputs though network</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>z2 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(X, <span style="color: #008000">self</span><span style="color: #666666">.</span>W1)
<span style="color: #008000">self</span><span style="color: #666666">.</span>a2 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>sigmoid(<span style="color: #008000">self</span><span style="color: #666666">.</span>z2)
<span style="color: #008000">self</span><span style="color: #666666">.</span>z3 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(<span style="color: #008000">self</span><span style="color: #666666">.</span>a2, <span style="color: #008000">self</span><span style="color: #666666">.</span>W2)
yHat <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>sigmoid(<span style="color: #008000">self</span><span style="color: #666666">.</span>z3)
<span style="color: #008000; font-weight: bold">return</span> yHat
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">sigmoid</span>(<span style="color: #008000">self</span>, z):
<span style="color: #408080; font-style: italic">#Apply sigmoid activation function to scalar, vector, or matrix</span>
<span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">1/</span>(<span style="color: #666666">1+</span>np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>z))
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">sigmoidPrime</span>(<span style="color: #008000">self</span>,z):
<span style="color: #408080; font-style: italic">#Gradient of sigmoid</span>
<span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>z)<span style="color: #666666">/</span>((<span style="color: #666666">1+</span>np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>z))<span style="color: #666666">**2</span>)
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">costFunction</span>(<span style="color: #008000">self</span>, X, y):
<span style="color: #408080; font-style: italic">#Compute cost for given X,y, use weights already stored in class.</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>yHat <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>forward(X)
J <span style="color: #666666">=</span> <span style="color: #666666">0.5*</span><span style="color: #008000">sum</span>((y<span style="color: #666666">-</span><span style="color: #008000">self</span><span style="color: #666666">.</span>yHat)<span style="color: #666666">**2</span>)<span style="color: #666666">/</span>X<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>] <span style="color: #666666">+</span> (<span style="color: #008000">self</span><span style="color: #666666">.</span>Lambda<span style="color: #666666">/2</span>)<span style="color: #666666">*</span>(np<span style="color: #666666">.</span>sum(<span style="color: #008000">self</span><span style="color: #666666">.</span>W1<span style="color: #666666">**2</span>)<span style="color: #666666">+</span>np<span style="color: #666666">.</span>sum(<span style="color: #008000">self</span><span style="color: #666666">.</span>W2<span style="color: #666666">**2</span>))
<span style="color: #008000; font-weight: bold">return</span> J
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">costFunctionPrime</span>(<span style="color: #008000">self</span>, X, y):
<span style="color: #408080; font-style: italic">#Compute derivative with respect to W and W2 for a given X and y:</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>yHat <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>forward(X)
delta3 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>multiply(<span style="color: #666666">-</span>(y<span style="color: #666666">-</span><span style="color: #008000">self</span><span style="color: #666666">.</span>yHat), <span style="color: #008000">self</span><span style="color: #666666">.</span>sigmoidPrime(<span style="color: #008000">self</span><span style="color: #666666">.</span>z3))
<span style="color: #408080; font-style: italic">#Add gradient of regularization term:</span>
dJdW2 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(<span style="color: #008000">self</span><span style="color: #666666">.</span>a2<span style="color: #666666">.</span>T, delta3)<span style="color: #666666">/</span>X<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>] <span style="color: #666666">+</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>Lambda<span style="color: #666666">*</span><span style="color: #008000">self</span><span style="color: #666666">.</span>W2
delta2 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(delta3, <span style="color: #008000">self</span><span style="color: #666666">.</span>W2<span style="color: #666666">.</span>T)<span style="color: #666666">*</span><span style="color: #008000">self</span><span style="color: #666666">.</span>sigmoidPrime(<span style="color: #008000">self</span><span style="color: #666666">.</span>z2)
<span style="color: #408080; font-style: italic">#Add gradient of regularization term:</span>
dJdW1 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>dot(X<span style="color: #666666">.</span>T, delta2)<span style="color: #666666">/</span>X<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>] <span style="color: #666666">+</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>Lambda<span style="color: #666666">*</span><span style="color: #008000">self</span><span style="color: #666666">.</span>W1
<span style="color: #008000; font-weight: bold">return</span> dJdW1, dJdW2
<span style="color: #408080; font-style: italic">#Helper functions for interacting with other methods/classes</span>
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">getParams</span>(<span style="color: #008000">self</span>):
<span style="color: #408080; font-style: italic">#Get W1 and W2 Rolled into vector:</span>
params <span style="color: #666666">=</span> np<span style="color: #666666">.</span>concatenate((<span style="color: #008000">self</span><span style="color: #666666">.</span>W1<span style="color: #666666">.</span>ravel(), <span style="color: #008000">self</span><span style="color: #666666">.</span>W2<span style="color: #666666">.</span>ravel()))
<span style="color: #008000; font-weight: bold">return</span> params
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">setParams</span>(<span style="color: #008000">self</span>, params):
<span style="color: #408080; font-style: italic">#Set W1 and W2 using single parameter vector:</span>
W1_start <span style="color: #666666">=</span> <span style="color: #666666">0</span>
W1_end <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>hiddenLayerSize<span style="color: #666666">*</span><span style="color: #008000">self</span><span style="color: #666666">.</span>inputLayerSize
<span style="color: #008000">self</span><span style="color: #666666">.</span>W1 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>reshape(params[W1_start:W1_end], \
(<span style="color: #008000">self</span><span style="color: #666666">.</span>inputLayerSize, <span style="color: #008000">self</span><span style="color: #666666">.</span>hiddenLayerSize))
W2_end <span style="color: #666666">=</span> W1_end <span style="color: #666666">+</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>hiddenLayerSize<span style="color: #666666">*</span><span style="color: #008000">self</span><span style="color: #666666">.</span>outputLayerSize
<span style="color: #008000">self</span><span style="color: #666666">.</span>W2 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>reshape(params[W1_end:W2_end], \
(<span style="color: #008000">self</span><span style="color: #666666">.</span>hiddenLayerSize, <span style="color: #008000">self</span><span style="color: #666666">.</span>outputLayerSize))
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">computeGradients</span>(<span style="color: #008000">self</span>, X, y):
dJdW1, dJdW2 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>costFunctionPrime(X, y)
<span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>concatenate((dJdW1<span style="color: #666666">.</span>ravel(), dJdW2<span style="color: #666666">.</span>ravel()))
<span style="color: #008000; font-weight: bold">class</span> <span style="color: #0000FF; font-weight: bold">trainer</span>(<span style="color: #008000">object</span>):
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">__init__</span>(<span style="color: #008000">self</span>, N):
<span style="color: #408080; font-style: italic">#Make Local reference to network:</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>N <span style="color: #666666">=</span> N
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">callbackF</span>(<span style="color: #008000">self</span>, params):
<span style="color: #008000">self</span><span style="color: #666666">.</span>N<span style="color: #666666">.</span>setParams(params)
<span style="color: #008000">self</span><span style="color: #666666">.</span>J<span style="color: #666666">.</span>append(<span style="color: #008000">self</span><span style="color: #666666">.</span>N<span style="color: #666666">.</span>costFunction(<span style="color: #008000">self</span><span style="color: #666666">.</span>X, <span style="color: #008000">self</span><span style="color: #666666">.</span>y))
<span style="color: #008000">self</span><span style="color: #666666">.</span>testJ<span style="color: #666666">.</span>append(<span style="color: #008000">self</span><span style="color: #666666">.</span>N<span style="color: #666666">.</span>costFunction(<span style="color: #008000">self</span><span style="color: #666666">.</span>testX, <span style="color: #008000">self</span><span style="color: #666666">.</span>testY))
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">costFunctionWrapper</span>(<span style="color: #008000">self</span>, params, X, y):
<span style="color: #008000">self</span><span style="color: #666666">.</span>N<span style="color: #666666">.</span>setParams(params)
cost <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>N<span style="color: #666666">.</span>costFunction(X, y)
grad <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>N<span style="color: #666666">.</span>computeGradients(X,y)
<span style="color: #008000; font-weight: bold">return</span> cost, grad
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">train</span>(<span style="color: #008000">self</span>, trainX, trainY, testX, testY):
<span style="color: #408080; font-style: italic">#Make an internal variable for the callback function:</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>X <span style="color: #666666">=</span> trainX
<span style="color: #008000">self</span><span style="color: #666666">.</span>y <span style="color: #666666">=</span> trainY
<span style="color: #008000">self</span><span style="color: #666666">.</span>testX <span style="color: #666666">=</span> testX
<span style="color: #008000">self</span><span style="color: #666666">.</span>testY <span style="color: #666666">=</span> testY
<span style="color: #408080; font-style: italic">#Make empty list to store training costs:</span>
<span style="color: #008000">self</span><span style="color: #666666">.</span>J <span style="color: #666666">=</span> []
<span style="color: #008000">self</span><span style="color: #666666">.</span>testJ <span style="color: #666666">=</span> []
params0 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>N<span style="color: #666666">.</span>getParams()
options <span style="color: #666666">=</span> {<span style="color: #BA2121">&#39;maxiter&#39;</span>: <span style="color: #666666">200</span>, <span style="color: #BA2121">&#39;disp&#39;</span> : <span style="color: #008000">True</span>}
_res <span style="color: #666666">=</span> optimize<span style="color: #666666">.</span>minimize(<span style="color: #008000">self</span><span style="color: #666666">.</span>costFunctionWrapper, params0, jac<span style="color: #666666">=</span><span style="color: #008000">True</span>, method<span style="color: #666666">=</span><span style="color: #BA2121">&#39;BFGS&#39;</span>, \
args<span style="color: #666666">=</span>(trainX, trainY), options<span style="color: #666666">=</span>options, callback<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>callbackF)
<span style="color: #008000">self</span><span style="color: #666666">.</span>N<span style="color: #666666">.</span>setParams(_res<span style="color: #666666">.</span>x)
<span style="color: #008000">self</span><span style="color: #666666">.</span>optimizationResults <span style="color: #666666">=</span> _res
</pre></div>
<p>
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