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mhjensen faf9db223a update week 42
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<h2 id="___sec32" class="anchor">Other Things to Try </h2>
<p>
Changing the size of the recurrent neural network and its parameters
can drastically change the results you get from the model. The below
code takes the simple recurrent neural network from above and adds a
second hidden layer, changes the number of neurons in the hidden
layer, and explicitly declares the activation function of the hidden
layers to be a sigmoid function. The loss function and optimizer can
also be changed but are kept the same as the above network. These
parameters can be tuned to provide the optimal result from the
network. For some ideas on how to improve the performance of a
<a href="https://danijar.com/tips-for-training-recurrent-neural-networks" target="_self">recurrent neural network</a>.
<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">rnn_2layers</span>(length_of_sequences, batch_size <span style="color: #666666">=</span> <span style="color: #008000; font-weight: bold">None</span>, stateful <span style="color: #666666">=</span> <span style="color: #008000; font-weight: bold">False</span>):
<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"> length_of_sequences (an int): the number of y values in &quot;x data&quot;. This is determined</span>
<span style="color: #BA2121; font-style: italic"> when the data is formatted</span>
<span style="color: #BA2121; font-style: italic"> batch_size (an int): Default value is None. See Keras documentation of SimpleRNN.</span>
<span style="color: #BA2121; font-style: italic"> stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN.</span>
<span style="color: #BA2121; font-style: italic"> Returns:</span>
<span style="color: #BA2121; font-style: italic"> model (a Keras model): The recurrent neural network that is built and compiled by this</span>
<span style="color: #BA2121; font-style: italic"> method</span>
<span style="color: #BA2121; font-style: italic"> Builds and compiles a recurrent neural network with two hidden layers and returns the model.</span>
<span style="color: #BA2121; font-style: italic"> &quot;&quot;&quot;</span>
<span style="color: #408080; font-style: italic"># Number of neurons in the input and output layers</span>
in_out_neurons <span style="color: #666666">=</span> <span style="color: #666666">1</span>
<span style="color: #408080; font-style: italic"># Number of neurons in the hidden layer, increased from the first network</span>
hidden_neurons <span style="color: #666666">=</span> <span style="color: #666666">500</span>
<span style="color: #408080; font-style: italic"># Define the input layer</span>
inp <span style="color: #666666">=</span> Input(batch_shape<span style="color: #666666">=</span>(batch_size,
length_of_sequences,
in_out_neurons))
<span style="color: #408080; font-style: italic"># Create two hidden layers instead of one hidden layer. Explicitly set the activation</span>
<span style="color: #408080; font-style: italic"># function to be the sigmoid function (the default value is hyperbolic tangent)</span>
rnn1 <span style="color: #666666">=</span> SimpleRNN(hidden_neurons,
return_sequences<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">True</span>, <span style="color: #408080; font-style: italic"># This needs to be True if another hidden layer is to follow</span>
stateful <span style="color: #666666">=</span> stateful, activation <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;sigmoid&#39;</span>,
name<span style="color: #666666">=</span><span style="color: #BA2121">&quot;RNN1&quot;</span>)(inp)
rnn2 <span style="color: #666666">=</span> SimpleRNN(hidden_neurons,
return_sequences<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>, activation <span style="color: #666666">=</span> <span style="color: #BA2121">&#39;sigmoid&#39;</span>,
stateful <span style="color: #666666">=</span> stateful,
name<span style="color: #666666">=</span><span style="color: #BA2121">&quot;RNN2&quot;</span>)(rnn1)
<span style="color: #408080; font-style: italic"># Define the output layer as a dense neural network layer (standard neural network layer)</span>
<span style="color: #408080; font-style: italic">#and add it to the network immediately after the hidden layer.</span>
dens <span style="color: #666666">=</span> Dense(in_out_neurons,name<span style="color: #666666">=</span><span style="color: #BA2121">&quot;dense&quot;</span>)(rnn2)
<span style="color: #408080; font-style: italic"># Create the machine learning model starting with the input layer and ending with the </span>
<span style="color: #408080; font-style: italic"># output layer</span>
model <span style="color: #666666">=</span> Model(inputs<span style="color: #666666">=</span>[inp],outputs<span style="color: #666666">=</span>[dens])
<span style="color: #408080; font-style: italic"># Compile the machine learning model using the mean squared error function as the loss </span>
<span style="color: #408080; font-style: italic"># function and an Adams optimizer.</span>
model<span style="color: #666666">.</span>compile(loss<span style="color: #666666">=</span><span style="color: #BA2121">&quot;mean_squared_error&quot;</span>, optimizer<span style="color: #666666">=</span><span style="color: #BA2121">&quot;adam&quot;</span>)
<span style="color: #008000; font-weight: bold">return</span> model
<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_2layers(length_of_sequences <span style="color: #666666">=</span> <span style="color: #666666">2</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: #408080; font-style: italic"># This section plots the training loss and the validation loss as a function of training iteration.</span>
<span style="color: #408080; font-style: italic"># This is not required for analyzing the couple cluster data but can help determine if the network is</span>
<span style="color: #408080; font-style: italic"># being overtrained.</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>
<p>
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