updated typos
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mhjensen
@@ -110,20 +110,19 @@ Automatically generated HTML file from DocOnce source
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('Improving performance', 2, None, '___sec44'),
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('Full object-oriented implementation', 2, None, '___sec45'),
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('Evaluate model performance on test data', 2, None, '___sec46'),
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('Adjust hyperparameters (if necessary, network architecture',
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2,
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None,
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'___sec47'),
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('scikit-learn implementation', 2, None, '___sec48'),
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('Adjust hyperparameters', 2, None, '___sec47'),
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('Visualization', 2, None, '___sec48'),
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('scikit-learn implementation', 2, None, '___sec49'),
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('Visualization', 2, None, '___sec50'),
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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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'___sec49'),
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('Tensorflow', 2, None, '___sec50'),
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('Collect and pre-process data', 2, None, '___sec51'),
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('Using TensorFlow backend', 2, None, '___sec52'),
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('Optimizing and using gradient descent', 2, None, '___sec53'),
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('Using Keras', 2, None, '___sec54')]}
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'___sec51'),
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('Tensorflow', 2, None, '___sec52'),
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('Collect and pre-process data', 2, None, '___sec53'),
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('Using TensorFlow backend', 2, None, '___sec54'),
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('Optimizing and using gradient descent', 2, None, '___sec55'),
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('Using Keras', 2, None, '___sec56')]}
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end of tocinfo -->
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<body>
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@@ -208,14 +207,16 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs045.html#___sec44" style="font-size: 80%;"><b>Improving performance</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs046.html#___sec45" style="font-size: 80%;"><b>Full object-oriented implementation</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs047.html#___sec46" style="font-size: 80%;"><b>Evaluate model performance on test data</b></a></li>
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<!-- navigation toc: --> <li><a href="#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters (if necessary, network architecture</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>scikit-learn implementation</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" 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-bs051.html#___sec50" style="font-size: 80%;"><b>Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs052.html#___sec51" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using Keras</b></a></li>
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<!-- navigation toc: --> <li><a href="#___sec47" style="font-size: 80%;"><b>Adjust hyperparameters</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs049.html#___sec48" style="font-size: 80%;"><b>Visualization</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs050.html#___sec49" style="font-size: 80%;"><b>scikit-learn implementation</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>Building neural networks in Tensorflow and Keras</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs053.html#___sec52" style="font-size: 80%;"><b>Tensorflow</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs054.html#___sec53" style="font-size: 80%;"><b>Collect and pre-process data</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs055.html#___sec54" style="font-size: 80%;"><b>Using TensorFlow backend</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs056.html#___sec55" style="font-size: 80%;"><b>Optimizing and using gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._NeuralNet-bs057.html#___sec56" style="font-size: 80%;"><b>Using Keras</b></a></li>
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</ul>
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</li>
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@@ -231,22 +232,18 @@ MathJax.Hub.Config({
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<a name="part0048"></a>
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<!-- !split -->
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<h2 id="___sec47" class="anchor">Adjust hyperparameters (if necessary, network architecture </h2>
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<h2 id="___sec47" class="anchor">Adjust hyperparameters </h2>
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<p>
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We now perform a grid search to find the optimal hyperparameters for the network.
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Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around \( 98 \% \) (\( 2 \% \) error rate).
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Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around \( 98\% \) (\( 2\% \) error rate).
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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>eta_vals <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-5</span>, <span style="color: #666666">1</span>, <span style="color: #666666">7</span>)
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lmbd_vals <span style="color: #666666">=</span> np<span style="color: #666666">.</span>logspace(<span style="color: #666666">-5</span>, <span style="color: #666666">1</span>, <span style="color: #666666">7</span>)
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</pre></div>
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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><span style="color: #408080; font-style: italic"># store the models for later use</span>
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<span style="color: #408080; font-style: italic"># store the models for later use</span>
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DNN_numpy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)), dtype<span style="color: #666666">=</span><span style="color: #008000">object</span>)
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<span style="color: #408080; font-style: italic"># grid search</span>
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@@ -266,44 +263,6 @@ DNN_numpy <span style="color: #666666">=</span> np<span style="color: #666666">.
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<span style="color: #008000; font-weight: bold">print</span>()
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</pre></div>
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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><span style="color: #408080; font-style: italic"># optional</span>
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<span style="color: #408080; font-style: italic"># visual representation of grid search</span>
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<span style="color: #408080; font-style: italic"># uses seaborn heatmap, I believe you can also do this with matplotlib imshow</span>
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<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">seaborn</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">sns</span>
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sns<span style="color: #666666">.</span>set()
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train_accuracy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)))
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test_accuracy <span style="color: #666666">=</span> np<span style="color: #666666">.</span>zeros((<span style="color: #008000">len</span>(eta_vals), <span style="color: #008000">len</span>(lmbd_vals)))
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<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(eta_vals)):
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<span style="color: #008000; font-weight: bold">for</span> j <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #008000">len</span>(lmbd_vals)):
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dnn <span style="color: #666666">=</span> DNN_numpy[i][j]
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train_pred <span style="color: #666666">=</span> dnn<span style="color: #666666">.</span>predict(X_train)
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test_pred <span style="color: #666666">=</span> dnn<span style="color: #666666">.</span>predict(X_test)
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train_accuracy[i][j] <span style="color: #666666">=</span> accuracy_score(Y_train, train_pred)
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test_accuracy[i][j] <span style="color: #666666">=</span> accuracy_score(Y_test, test_pred)
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fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(figsize <span style="color: #666666">=</span> (<span style="color: #666666">10</span>, <span style="color: #666666">10</span>))
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sns<span style="color: #666666">.</span>heatmap(train_accuracy, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>, ax<span style="color: #666666">=</span>ax, cmap<span style="color: #666666">=</span><span style="color: #BA2121">"viridis"</span>)
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ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Training Accuracy"</span>)
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ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
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ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
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plt<span style="color: #666666">.</span>show()
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fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(figsize <span style="color: #666666">=</span> (<span style="color: #666666">10</span>, <span style="color: #666666">10</span>))
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sns<span style="color: #666666">.</span>heatmap(test_accuracy, annot<span style="color: #666666">=</span><span style="color: #008000">True</span>, ax<span style="color: #666666">=</span>ax, cmap<span style="color: #666666">=</span><span style="color: #BA2121">"viridis"</span>)
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ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Test Accuracy"</span>)
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ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
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ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
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plt<span style="color: #666666">.</span>show()
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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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<ul class="pagination">
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@@ -326,6 +285,8 @@ plt<span style="color: #666666">.</span>show()
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<li><a href="._NeuralNet-bs053.html">54</a></li>
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<li><a href="._NeuralNet-bs054.html">55</a></li>
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<li><a href="._NeuralNet-bs055.html">56</a></li>
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<li><a href="._NeuralNet-bs056.html">57</a></li>
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<li><a href="._NeuralNet-bs057.html">58</a></li>
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</ul>
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