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<a class="navbar-brand" href="week43-bs.html">Week 43: Deep Learning: Recurrent Neural Networks and other Deep Learning Methods. Principal Component analysis</a>
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<!-- navigation toc: --> <li><a href="._week43-bs001.html#___sec0" style="font-size: 80%;"><b>Plans for week 43</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Reading Recommendations</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Summary on Deep Learning Methods</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>CNNs in brief</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>Recurrent neural networks: Overarching view</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs006.html#___sec5" style="font-size: 80%;"><b>Set up of an RNN</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs008.html#___sec7" style="font-size: 80%;"><b>An extrapolation example</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>Formatting the Data</b></a></li>
<!-- navigation toc: --> <li><a href="#___sec9" style="font-size: 80%;"><b>Predicting New Points With A Trained Recurrent Neural Network</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Other Things to Try</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs012.html#___sec11" style="font-size: 80%;"><b>Other Types of Recurrent Neural Networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs019.html#___sec18" style="font-size: 80%;"><b>Writing Our First Generative Adversarial Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs022.html#___sec21" style="font-size: 80%;"><b>Training Step</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>Checkpoints</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>Exploring the Latent Space</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Getting Results</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Interpolating Between MNIST Digits</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs027.html#___sec26" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>More on the covariance</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Reminding ourselves about Linear Regression</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>Simple Example</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs032.html#___sec31" style="font-size: 80%;"><b>The Correlation Matrix</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs035.html#___sec34" style="font-size: 80%;"><b>Using Pandas</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs036.html#___sec35" style="font-size: 80%;"><b>And then the Franke Function</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs039.html#___sec38" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs041.html#___sec40" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Implementing it</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>First Step</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Scaling</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>Centered Data</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>Exploring</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs048.html#___sec47" style="font-size: 80%;"><b>Diagonalize the sample covariance matrix to obtain the principal components</b></a></li>
<!-- navigation toc: --> <li><a href="._week43-bs049.html#___sec48" style="font-size: 80%;"><b>Collecting all Steps</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs051.html#___sec50" style="font-size: 80%;"><b>The PCA Theorem</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec55" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Randomized PCA</a></li>
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<h2 id="___sec9" class="anchor">Predicting New Points With A Trained Recurrent Neural Network </h2>
<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">def</span> <span style="color: #0000FF">test_rnn</span> (x1, y_test, plot_min, plot_max):
<span style="color: #BA2121; font-style: italic">&quot;&quot;&quot;</span>
<span style="color: #BA2121; font-style: italic"> Inputs:</span>
<span style="color: #BA2121; font-style: italic"> x1 (a list or numpy array): The complete x component of the data set</span>
<span style="color: #BA2121; font-style: italic"> y_test (a list or numpy array): The complete y component of the data set</span>
<span style="color: #BA2121; font-style: italic"> plot_min (an int or float): the smallest x value used in the training data</span>
<span style="color: #BA2121; font-style: italic"> plot_max (an int or float): the largest x valye used in the training data</span>
<span style="color: #BA2121; font-style: italic"> Returns:</span>
<span style="color: #BA2121; font-style: italic"> None.</span>
<span style="color: #BA2121; font-style: italic"> Uses a trained recurrent neural network model to predict future points in the </span>
<span style="color: #BA2121; font-style: italic"> series. Computes the MSE of the predicted data set from the true data set, saves</span>
<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>
<span style="color: #BA2121; font-style: italic"> while also displaying the data range used for training.</span>
<span style="color: #BA2121; font-style: italic"> &quot;&quot;&quot;</span>
<span style="color: #408080; font-style: italic"># Add the training data as the first dim points in the predicted data array as these</span>
<span style="color: #408080; font-style: italic"># are known values.</span>
y_pred <span style="color: #666666">=</span> y_test[:dim]<span style="color: #666666">.</span>tolist()
<span style="color: #408080; font-style: italic"># Generate the first input to the trained recurrent neural network using the last two </span>
<span style="color: #408080; font-style: italic"># points of the training data. Based on how the network was trained this means that it</span>
<span style="color: #408080; font-style: italic"># will predict the first point in the data set after the training data. All of the </span>
<span style="color: #408080; font-style: italic"># brackets are necessary for Tensorflow.</span>
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>]]]])
<span style="color: #408080; font-style: italic"># Save the very last point in the training data set. This will be used later.</span>
last <span style="color: #666666">=</span> [y_test[dim<span style="color: #666666">-1</span>]]
<span style="color: #408080; font-style: italic"># Iterate until the complete data set is created.</span>
<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)):
<span style="color: #408080; font-style: italic"># Predict the next point in the data set using the previous two points.</span>
<span style="color: #008000">next</span> <span style="color: #666666">=</span> model<span style="color: #666666">.</span>predict(next_input)
<span style="color: #408080; font-style: italic"># Append just the number of the predicted data set</span>
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>])
<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>
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)
last <span style="color: #666666">=</span> <span style="color: #008000">next</span>
<span style="color: #408080; font-style: italic"># Print the mean squared error between the known data set and the predicted data set.</span>
<span style="color: #008000">print</span>(<span style="color: #BA2121">&#39;MSE: &#39;</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())
<span style="color: #408080; font-style: italic"># Save the predicted data set as a csv file for later use</span>
name <span style="color: #666666">=</span> datatype <span style="color: #666666">+</span> <span style="color: #BA2121">&#39;Predicted&#39;</span><span style="color: #666666">+</span><span style="color: #008000">str</span>(dim)<span style="color: #666666">+</span><span style="color: #BA2121">&#39;.csv&#39;</span>
np<span style="color: #666666">.</span>savetxt(name, y_pred, delimiter<span style="color: #666666">=</span><span style="color: #BA2121">&#39;,&#39;</span>)
<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>
<span style="color: #408080; font-style: italic"># for the training data.</span>
fig, ax <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots()
ax<span style="color: #666666">.</span>plot(x1, y_test, label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;true&quot;</span>, linewidth<span style="color: #666666">=3</span>)
ax<span style="color: #666666">.</span>plot(x1, y_pred, <span style="color: #BA2121">&#39;g-.&#39;</span>,label<span style="color: #666666">=</span><span style="color: #BA2121">&quot;predicted&quot;</span>, linewidth<span style="color: #666666">=4</span>)
ax<span style="color: #666666">.</span>legend()
<span style="color: #408080; font-style: italic"># Created a red region to represent the points used in the training data.</span>
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">&#39;red&#39;</span>)
plt<span style="color: #666666">.</span>show()
<span style="color: #408080; font-style: italic"># Check to make sure the data set is complete</span>
<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)
<span style="color: #408080; font-style: italic"># This is the number of points that will be used in as the training data</span>
dim<span style="color: #666666">=12</span>
<span style="color: #408080; font-style: italic"># Separate the training data from the whole data set</span>
X_train <span style="color: #666666">=</span> X_tot[:dim]
y_train <span style="color: #666666">=</span> y_tot[:dim]
<span style="color: #408080; font-style: italic"># Generate the training data for the RNN, using a sequence of 2</span>
rnn_input, rnn_training <span style="color: #666666">=</span> format_data(y_train, <span style="color: #666666">2</span>)
<span style="color: #408080; font-style: italic"># Create a recurrent neural network in Keras and produce a summary of the </span>
<span style="color: #408080; font-style: italic"># machine learning model</span>
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>])
model<span style="color: #666666">.</span>summary()
<span style="color: #408080; font-style: italic"># Start the timer. Want to time training+testing</span>
start <span style="color: #666666">=</span> timer()
<span style="color: #408080; font-style: italic"># Fit the model using the training data genenerated above using 150 training iterations and a 5%</span>
<span style="color: #408080; font-style: italic"># validation split. Setting verbose to True prints information about each training iteration.</span>
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>,
verbose<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>,validation_split<span style="color: #666666">=0.05</span>)
<span style="color: #008000; font-weight: bold">for</span> label <span style="color: #AA22FF; font-weight: bold">in</span> [<span style="color: #BA2121">&quot;loss&quot;</span>,<span style="color: #BA2121">&quot;val_loss&quot;</span>]:
plt<span style="color: #666666">.</span>plot(hist<span style="color: #666666">.</span>history[label],label<span style="color: #666666">=</span>label)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">&quot;loss&quot;</span>)
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">&quot;epoch&quot;</span>)
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">&quot;The final validation loss: </span><span style="color: #BB6688; font-weight: bold">{}</span><span style="color: #BA2121">&quot;</span><span style="color: #666666">.</span>format(hist<span style="color: #666666">.</span>history[<span style="color: #BA2121">&quot;val_loss&quot;</span>][<span style="color: #666666">-1</span>]))
plt<span style="color: #666666">.</span>legend()
plt<span style="color: #666666">.</span>show()
<span style="color: #408080; font-style: italic"># Use the trained neural network to predict more points of the data set</span>
test_rnn(X_tot, y_tot, X_tot[<span style="color: #666666">0</span>], X_tot[dim<span style="color: #666666">-1</span>])
<span style="color: #408080; font-style: italic"># Stop the timer and calculate the total time needed.</span>
end <span style="color: #666666">=</span> timer()
<span style="color: #008000">print</span>(<span style="color: #BA2121">&#39;Time: &#39;</span>, end<span style="color: #666666">-</span>start)
</pre></div>
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