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370 lines
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<!-- navigation toc: --> <li><a href="._week45-bs001.html#plan-for-week-45" style="font-size: 80%;"><b>Plan for week 45</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs002.html#material-for-the-lab-sessions-additional-ways-to-present-classification-results-and-other-practicalities" style="font-size: 80%;"><b>Material for the lab sessions, additional ways to present classification results and other practicalities</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs003.html#searching-for-optimal-regularization-parameters-lambda" style="font-size: 80%;"><b>Searching for Optimal Regularization Parameters \( \lambda \)</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs009.html#other-ways-of-presenting-a-classification-problem" style="font-size: 80%;"><b>Other ways of presenting a classification problem</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs010.html#combinations-of-classification-results" style="font-size: 80%;"><b>Combinations of classification results</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs011.html#positive-and-negative-prediction-values" style="font-size: 80%;"><b>Positive and negative prediction values</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs013.html#f-1-score" style="font-size: 80%;"><b>\( F_1 \) score</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs014.html#roc-curve" style="font-size: 80%;"><b>ROC curve</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs015.html#cumulative-gain-curve" style="font-size: 80%;"><b>Cumulative gain curve</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs016.html#other-measures-in-classification-studies-cancer-data-again" style="font-size: 80%;"><b>Other measures in classification studies: Cancer Data again</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs017.html#material-for-lecture-thursday-november-9" style="font-size: 80%;"><b>Material for Lecture Thursday November 9</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs018.html#recurrent-neural-networks-rnns-overarching-view" style="font-size: 80%;"><b>Recurrent neural networks (RNNs): Overarching view</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs019.html#a-simple-example" style="font-size: 80%;"><b>A simple example</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs019.html#rnns" style="font-size: 80%;"> RNNs</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#basic-layout" style="font-size: 80%;"><b>Basic layout</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#we-need-to-specify-the-initial-activity-state-of-all-the-hidden-and-output-units" style="font-size: 80%;"> We need to specify the initial activity state of all the hidden and output units</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#we-can-specify-inputs-in-several-ways" style="font-size: 80%;"> We can specify inputs in several ways</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#we-can-specify-targets-in-several-ways" style="font-size: 80%;"> We can specify targets in several ways</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#backpropagation-through-time" style="font-size: 80%;"> Backpropagation through time</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs020.html#the-backward-pass-is-linear" style="font-size: 80%;"> The backward pass is linear</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs022.html#four-effective-ways-to-learn-an-rnn" style="font-size: 80%;"><b>Four effective ways to learn an RNN</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs022.html#long-short-term-memory-lstm" style="font-size: 80%;"> Long Short Term Memory (LSTM)</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs022.html#implementing-a-memory-cell-in-a-neural-network" style="font-size: 80%;"> Implementing a memory cell in a neural network</a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs023.html#an-extrapolation-example" style="font-size: 80%;"><b>An extrapolation example</b></a></li>
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<!-- navigation toc: --> <li><a href="#predicting-new-points-with-a-trained-recurrent-neural-network" style="font-size: 80%;"><b>Predicting New Points With A Trained Recurrent Neural Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs026.html#other-things-to-try" style="font-size: 80%;"><b>Other Things to Try</b></a></li>
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<!-- navigation toc: --> <li><a href="._week45-bs027.html#other-types-of-recurrent-neural-networks" style="font-size: 80%;"><b>Other Types of Recurrent Neural Networks</b></a></li>
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<h2 id="predicting-new-points-with-a-trained-recurrent-neural-network" class="anchor">Predicting New Points With A Trained Recurrent Neural Network </h2>
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<pre style="line-height: 125%;"><span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">test_rnn</span> (x1, y_test, plot_min, plot_max):
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<span style="color: #BA2121; font-style: italic">"""</span>
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<span style="color: #BA2121; font-style: italic"> Inputs:</span>
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<span style="color: #BA2121; font-style: italic"> x1 (a list or numpy array): The complete x component of the data set</span>
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<span style="color: #BA2121; font-style: italic"> y_test (a list or numpy array): The complete y component of the data set</span>
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<span style="color: #BA2121; font-style: italic"> plot_min (an int or float): the smallest x value used in the training data</span>
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<span style="color: #BA2121; font-style: italic"> plot_max (an int or float): the largest x valye used in the training data</span>
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<span style="color: #BA2121; font-style: italic"> Returns:</span>
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<span style="color: #BA2121; font-style: italic"> None.</span>
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<span style="color: #BA2121; font-style: italic"> Uses a trained recurrent neural network model to predict future points in the </span>
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<span style="color: #BA2121; font-style: italic"> series. Computes the MSE of the predicted data set from the true data set, saves</span>
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<span style="color: #BA2121; font-style: italic"> the predicted data set to a csv file, and plots the predicted and true data sets w</span>
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<span style="color: #BA2121; font-style: italic"> while also displaying the data range used for training.</span>
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<span style="color: #BA2121; font-style: italic"> """</span>
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<span style="color: #408080; font-style: italic"># Add the training data as the first dim points in the predicted data array as these</span>
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<span style="color: #408080; font-style: italic"># are known values.</span>
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y_pred <span style="color: #666666">=</span> y_test[:dim]<span style="color: #666666">.</span>tolist()
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<span style="color: #408080; font-style: italic"># Generate the first input to the trained recurrent neural network using the last two </span>
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<span style="color: #408080; font-style: italic"># points of the training data. Based on how the network was trained this means that it</span>
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<span style="color: #408080; font-style: italic"># will predict the first point in the data set after the training data. All of the </span>
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<span style="color: #408080; font-style: italic"># brackets are necessary for Tensorflow.</span>
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next_input <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[[y_test[dim<span style="color: #666666">-2</span>]], [y_test[dim<span style="color: #666666">-1</span>]]]])
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<span style="color: #408080; font-style: italic"># Save the very last point in the training data set. This will be used later.</span>
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last <span style="color: #666666">=</span> [y_test[dim<span style="color: #666666">-1</span>]]
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<span style="color: #408080; font-style: italic"># Iterate until the complete data set is created.</span>
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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> (dim, <span style="color: #008000">len</span>(y_test)):
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<span style="color: #408080; font-style: italic"># Predict the next point in the data set using the previous two points.</span>
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<span style="color: #008000">next</span> <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(next_input)
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<span style="color: #408080; font-style: italic"># Append just the number of the predicted data set</span>
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y_pred<span style="color: #666666">.</span>append(<span style="color: #008000">next</span>[<span style="color: #666666">0</span>][<span style="color: #666666">0</span>])
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<span style="color: #408080; font-style: italic"># Create the input that will be used to predict the next data point in the data set.</span>
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next_input <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[last, <span style="color: #008000">next</span>[<span style="color: #666666">0</span>]]], dtype<span style="color: #666666">=</span>np<span style="color: #666666">.</span>float64)
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last <span style="color: #666666">=</span> <span style="color: #008000">next</span>
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<span style="color: #408080; font-style: italic"># Print the mean squared error between the known data set and the predicted data set.</span>
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<span style="color: #008000">print</span>(<span style="color: #BA2121">'MSE: '</span>, np<span style="color: #666666">.</span>square(np<span style="color: #666666">.</span>subtract(y_test, y_pred))<span style="color: #666666">.</span>mean())
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<span style="color: #408080; font-style: italic"># Save the predicted data set as a csv file for later use</span>
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name <span style="color: #666666">=</span> datatype <span style="color: #666666">+</span> <span style="color: #BA2121">'Predicted'</span><span style="color: #666666">+</span><span style="color: #008000">str</span>(dim)<span style="color: #666666">+</span><span style="color: #BA2121">'.csv'</span>
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np<span style="color: #666666">.</span>savetxt(name, y_pred, delimiter<span style="color: #666666">=</span><span style="color: #BA2121">','</span>)
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<span style="color: #408080; font-style: italic"># Plot the known data set and the predicted data set. The red box represents the region that was used</span>
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<span style="color: #408080; font-style: italic"># for the training data.</span>
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fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots()
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ax<span style="color: #666666">.</span>plot(x1, y_test, label<span style="color: #666666">=</span><span style="color: #BA2121">"true"</span>, linewidth<span style="color: #666666">=3</span>)
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ax<span style="color: #666666">.</span>plot(x1, y_pred, <span style="color: #BA2121">'g-.'</span>,label<span style="color: #666666">=</span><span style="color: #BA2121">"predicted"</span>, linewidth<span style="color: #666666">=4</span>)
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ax<span style="color: #666666">.</span>legend()
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<span style="color: #408080; font-style: italic"># Created a red region to represent the points used in the training data.</span>
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ax<span style="color: #666666">.</span>axvspan(plot_min, plot_max, alpha<span style="color: #666666">=0.25</span>, color<span style="color: #666666">=</span><span style="color: #BA2121">'red'</span>)
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plt<span style="color: #666666">.</span>show()
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<span style="color: #408080; font-style: italic"># Check to make sure the data set is complete</span>
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<span style="color: #008000; font-weight: bold">assert</span> <span style="color: #008000">len</span>(X_tot) <span style="color: #666666">==</span> <span style="color: #008000">len</span>(y_tot)
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<span style="color: #408080; font-style: italic"># This is the number of points that will be used in as the training data</span>
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dim<span style="color: #666666">=12</span>
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<span style="color: #408080; font-style: italic"># Separate the training data from the whole data set</span>
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X_train <span style="color: #666666">=</span> X_tot[:dim]
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y_train <span style="color: #666666">=</span> y_tot[:dim]
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<span style="color: #408080; font-style: italic"># Generate the training data for the RNN, using a sequence of 2</span>
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rnn_input, rnn_training <span style="color: #666666">=</span> format_data(y_train, <span style="color: #666666">2</span>)
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<span style="color: #408080; font-style: italic"># Create a recurrent neural network in Keras and produce a summary of the </span>
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<span style="color: #408080; font-style: italic"># machine learning model</span>
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model <span style="color: #666666">=</span> rnn(length_of_sequences <span style="color: #666666">=</span> rnn_input<span style="color: #666666">.</span>shape[<span style="color: #666666">1</span>])
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model<span style="color: #666666">.</span>summary()
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<span style="color: #408080; font-style: italic"># Start the timer. Want to time training+testing</span>
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start <span style="color: #666666">=</span> timer()
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<span style="color: #408080; font-style: italic"># Fit the model using the training data genenerated above using 150 training iterations and a 5%</span>
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<span style="color: #408080; font-style: italic"># validation split. Setting verbose to True prints information about each training iteration.</span>
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hist <span style="color: #666666">=</span> model<span style="color: #666666">.</span>fit(rnn_input, rnn_training, batch_size<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">None</span>, epochs<span style="color: #666666">=150</span>,
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verbose<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>,validation_split<span style="color: #666666">=0.05</span>)
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<span style="color: #008000; font-weight: bold">for</span> label <span style="color: #AA22FF; font-weight: bold">in</span> [<span style="color: #BA2121">"loss"</span>,<span style="color: #BA2121">"val_loss"</span>]:
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plt<span style="color: #666666">.</span>plot(hist<span style="color: #666666">.</span>history[label],label<span style="color: #666666">=</span>label)
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plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"loss"</span>)
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plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">"epoch"</span>)
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plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"The final validation loss: </span><span style="color: #BB6688; font-weight: bold">{}</span><span style="color: #BA2121">"</span><span style="color: #666666">.</span>format(hist<span style="color: #666666">.</span>history[<span style="color: #BA2121">"val_loss"</span>][<span style="color: #666666">-1</span>]))
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plt<span style="color: #666666">.</span>legend()
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plt<span style="color: #666666">.</span>show()
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<span style="color: #408080; font-style: italic"># Use the trained neural network to predict more points of the data set</span>
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test_rnn(X_tot, y_tot, X_tot[<span style="color: #666666">0</span>], X_tot[dim<span style="color: #666666">-1</span>])
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<span style="color: #408080; font-style: italic"># Stop the timer and calculate the total time needed.</span>
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end <span style="color: #666666">=</span> timer()
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<span style="color: #008000">print</span>(<span style="color: #BA2121">'Time: '</span>, end<span style="color: #666666">-</span>start)
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</pre>
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