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('Reading Recommendations', 2, None, '___sec1'),
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('Summary on Deep Learning Methods', 2, None, '___sec2'),
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('CNNs in brief', 2, None, '___sec3'),
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('Set up of an RNN', 2, None, '___sec5'),
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('Writing Our First Generative Adversarial Network',
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('Other Models', 2, None, '___sec20'),
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('The Correlation Matrix', 2, None, '___sec31'),
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('Correlation Matrix again', 2, None, '___sec33'),
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('Using Pandas', 2, None, '___sec34'),
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('And then the Franke Function', 2, None, '___sec35'),
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('Lnks with the Design Matrix', 2, None, '___sec36'),
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('Computing the Expectation Values', 2, None, '___sec37'),
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('Towards the PCA theorem', 2, None, '___sec38'),
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('More on the PCA Theorem', 2, None, '___sec39'),
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('The Algorithm before the Theorem', 2, None, '___sec40'),
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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>
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<!-- navigation toc: --> <li><a href="._week43-bs002.html#___sec1" style="font-size: 80%;"><b>Reading Recommendations</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs003.html#___sec2" style="font-size: 80%;"><b>Summary on Deep Learning Methods</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs004.html#___sec3" style="font-size: 80%;"><b>CNNs in brief</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs005.html#___sec4" style="font-size: 80%;"><b>Recurrent neural networks: Overarching view</b></a></li>
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<!-- 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-bs007.html#___sec6" style="font-size: 80%;"><b>A simple example</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>
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<!-- navigation toc: --> <li><a href="._week43-bs009.html#___sec8" style="font-size: 80%;"><b>Formatting the Data</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs010.html#___sec9" 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="._week43-bs011.html#___sec10" style="font-size: 80%;"><b>Other Things to Try</b></a></li>
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<!-- 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-bs013.html#___sec12" style="font-size: 80%;"><b>Generative Models</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs014.html#___sec13" style="font-size: 80%;"><b>Generative Adversarial Networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs015.html#___sec14" style="font-size: 80%;"><b>Discriminator</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs016.html#___sec15" style="font-size: 80%;"><b>Learning Process</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs017.html#___sec16" style="font-size: 80%;"><b>More about the Learning Process</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs018.html#___sec17" style="font-size: 80%;"><b>Additional References</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="#___sec19" style="font-size: 80%;"><b>MNIST and GANs</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs021.html#___sec20" style="font-size: 80%;"><b>Other Models</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>
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<!-- navigation toc: --> <li><a href="._week43-bs023.html#___sec22" style="font-size: 80%;"><b>Checkpoints</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs024.html#___sec23" style="font-size: 80%;"><b>Exploring the Latent Space</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs025.html#___sec24" style="font-size: 80%;"><b>Getting Results</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs026.html#___sec25" style="font-size: 80%;"><b>Interpolating Between MNIST Digits</b></a></li>
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<!-- 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>
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<!-- navigation toc: --> <li><a href="._week43-bs028.html#___sec27" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs029.html#___sec28" style="font-size: 80%;"><b>More on the covariance</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs030.html#___sec29" style="font-size: 80%;"><b>Reminding ourselves about Linear Regression</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs031.html#___sec30" style="font-size: 80%;"><b>Simple Example</b></a></li>
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<!-- 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-bs033.html#___sec32" style="font-size: 80%;"><b>Numpy Functionality</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs034.html#___sec33" style="font-size: 80%;"><b>Correlation Matrix again</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>
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<!-- 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-bs037.html#___sec36" style="font-size: 80%;"><b>Lnks with the Design Matrix</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs038.html#___sec37" style="font-size: 80%;"><b>Computing the Expectation Values</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-bs040.html#___sec39" style="font-size: 80%;"><b>More on 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>
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<!-- navigation toc: --> <li><a href="._week43-bs042.html#___sec41" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs043.html#___sec42" style="font-size: 80%;"><b>Implementing it</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs044.html#___sec43" style="font-size: 80%;"><b>First Step</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs045.html#___sec44" style="font-size: 80%;"><b>Scaling</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs046.html#___sec45" style="font-size: 80%;"><b>Centered Data</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs047.html#___sec46" style="font-size: 80%;"><b>Exploring</b></a></li>
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<!-- 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>
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<!-- 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-bs050.html#___sec49" style="font-size: 80%;"><b>Classical PCA Theorem</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-bs052.html#___sec51" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs053.html#___sec52" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs054.html#___sec53" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec54" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec55" style="font-size: 80%;"> Randomized PCA</a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs055.html#___sec56" style="font-size: 80%;"> Kernel PCA</a></li>
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<!-- navigation toc: --> <li><a href="._week43-bs056.html#___sec57" style="font-size: 80%;"><b>Other techniques</b></a></li>
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</li>
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<div class="container">
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0020"></a>
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<!-- !split -->
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<h2 id="___sec19" class="anchor">MNIST and GANs </h2>
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<p>
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Let's have a quick look
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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>plt<span style="color: #666666">.</span>imshow(train_images[<span style="color: #666666">0</span>], cmap<span style="color: #666666">=</span><span style="color: #BA2121">'Greys'</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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Now we define our two models. This is where the 'magic' happens. There are a
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huge amount of possible formulations for both models. A lot of engineering and
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trial and error can be done here to try to produce better performing models. For
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more advanced GANs this is by far the step where you can 'make or break' a
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model.
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<p>
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We start with the generator. As stated in the introductory text the generator
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\( g \) upsamples from a random sample to the shape of what we want to predict. In
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our case we are trying to predict MNIST images (\( 28\times 28 \) pixels).
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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: #008000; font-weight: bold">def</span> <span style="color: #0000FF">generator_model</span>():
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<span style="color: #BA2121; font-style: italic">"""</span>
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<span style="color: #BA2121; font-style: italic"> The generator uses upsampling layers tf.keras.layers.Conv2DTranspose() to</span>
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<span style="color: #BA2121; font-style: italic"> produce an image from a random seed. We start with a Dense layer taking this</span>
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<span style="color: #BA2121; font-style: italic"> random sample as an input and subsequently upsample through multiple</span>
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<span style="color: #BA2121; font-style: italic"> convolutional layers.</span>
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<span style="color: #BA2121; font-style: italic"> """</span>
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<span style="color: #408080; font-style: italic"># we define our model</span>
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model <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>keras<span style="color: #666666">.</span>Sequential()
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<span style="color: #408080; font-style: italic"># adding our input layer. Dense means that every neuron is connected and</span>
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<span style="color: #408080; font-style: italic"># the input shape is the shape of our random noise. The units need to match</span>
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<span style="color: #408080; font-style: italic"># in some sense the upsampling strides to reach our desired output shape.</span>
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<span style="color: #408080; font-style: italic"># we are using 100 random numbers as our seed</span>
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model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Dense(units<span style="color: #666666">=7*7*</span>BATCH_SIZE,
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use_bias<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>,
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input_shape<span style="color: #666666">=</span>(<span style="color: #666666">100</span>, )))
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<span style="color: #408080; font-style: italic"># we normalize the output form the Dense layer</span>
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model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>BatchNormalization())
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<span style="color: #408080; font-style: italic"># and add an activation function to our 'layer'. LeakyReLU avoids vanishing</span>
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<span style="color: #408080; font-style: italic"># gradient problem</span>
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model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>LeakyReLU())
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model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Reshape((<span style="color: #666666">7</span>, <span style="color: #666666">7</span>, BATCH_SIZE)))
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<span style="color: #008000; font-weight: bold">assert</span> model<span style="color: #666666">.</span>output_shape <span style="color: #666666">==</span> (<span style="color: #008000; font-weight: bold">None</span>, <span style="color: #666666">7</span>, <span style="color: #666666">7</span>, BATCH_SIZE)
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<span style="color: #408080; font-style: italic"># even though we just added four keras layers we think of everything above</span>
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<span style="color: #408080; font-style: italic"># as 'one' layer</span>
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<span style="color: #408080; font-style: italic"># next we add our upscaling convolutional layers</span>
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model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Conv2DTranspose(filters<span style="color: #666666">=128</span>,
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kernel_size<span style="color: #666666">=</span>(<span style="color: #666666">5</span>, <span style="color: #666666">5</span>),
|
|
strides<span style="color: #666666">=</span>(<span style="color: #666666">1</span>, <span style="color: #666666">1</span>),
|
|
padding<span style="color: #666666">=</span><span style="color: #BA2121">'same'</span>,
|
|
use_bias<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>))
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>BatchNormalization())
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>LeakyReLU())
|
|
<span style="color: #008000; font-weight: bold">assert</span> model<span style="color: #666666">.</span>output_shape <span style="color: #666666">==</span> (<span style="color: #008000; font-weight: bold">None</span>, <span style="color: #666666">7</span>, <span style="color: #666666">7</span>, <span style="color: #666666">128</span>)
|
|
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Conv2DTranspose(filters<span style="color: #666666">=64</span>,
|
|
kernel_size<span style="color: #666666">=</span>(<span style="color: #666666">5</span>, <span style="color: #666666">5</span>),
|
|
strides<span style="color: #666666">=</span>(<span style="color: #666666">2</span>, <span style="color: #666666">2</span>),
|
|
padding<span style="color: #666666">=</span><span style="color: #BA2121">'same'</span>,
|
|
use_bias<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>))
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>BatchNormalization())
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>LeakyReLU())
|
|
<span style="color: #008000; font-weight: bold">assert</span> model<span style="color: #666666">.</span>output_shape <span style="color: #666666">==</span> (<span style="color: #008000; font-weight: bold">None</span>, <span style="color: #666666">14</span>, <span style="color: #666666">14</span>, <span style="color: #666666">64</span>)
|
|
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Conv2DTranspose(filters<span style="color: #666666">=1</span>,
|
|
kernel_size<span style="color: #666666">=</span>(<span style="color: #666666">5</span>, <span style="color: #666666">5</span>),
|
|
strides<span style="color: #666666">=</span>(<span style="color: #666666">2</span>, <span style="color: #666666">2</span>),
|
|
padding<span style="color: #666666">=</span><span style="color: #BA2121">'same'</span>,
|
|
use_bias<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">False</span>,
|
|
activation<span style="color: #666666">=</span><span style="color: #BA2121">'tanh'</span>))
|
|
<span style="color: #008000; font-weight: bold">assert</span> model<span style="color: #666666">.</span>output_shape <span style="color: #666666">==</span> (<span style="color: #008000; font-weight: bold">None</span>, <span style="color: #666666">28</span>, <span style="color: #666666">28</span>, <span style="color: #666666">1</span>)
|
|
|
|
<span style="color: #008000; font-weight: bold">return</span> model
|
|
</pre></div>
|
|
<p>
|
|
And there we have our 'simple' generator model. Now we move on to defining our
|
|
discriminator model \( d \), which is a convolutional neural network based image
|
|
classifier.
|
|
|
|
<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">discriminator_model</span>():
|
|
<span style="color: #BA2121; font-style: italic">"""</span>
|
|
<span style="color: #BA2121; font-style: italic"> The discriminator is a convolutional neural network based image classifier</span>
|
|
<span style="color: #BA2121; font-style: italic"> """</span>
|
|
|
|
<span style="color: #408080; font-style: italic"># we define our model</span>
|
|
model <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>keras<span style="color: #666666">.</span>Sequential()
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Conv2D(filters<span style="color: #666666">=64</span>,
|
|
kernel_size<span style="color: #666666">=</span>(<span style="color: #666666">5</span>, <span style="color: #666666">5</span>),
|
|
strides<span style="color: #666666">=</span>(<span style="color: #666666">2</span>, <span style="color: #666666">2</span>),
|
|
padding<span style="color: #666666">=</span><span style="color: #BA2121">'same'</span>,
|
|
input_shape<span style="color: #666666">=</span>[<span style="color: #666666">28</span>, <span style="color: #666666">28</span>, <span style="color: #666666">1</span>]))
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>LeakyReLU())
|
|
<span style="color: #408080; font-style: italic"># adding a dropout layer as you do in conv-nets</span>
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Dropout(<span style="color: #666666">0.3</span>))
|
|
|
|
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Conv2D(filters<span style="color: #666666">=128</span>,
|
|
kernel_size<span style="color: #666666">=</span>(<span style="color: #666666">5</span>, <span style="color: #666666">5</span>),
|
|
strides<span style="color: #666666">=</span>(<span style="color: #666666">2</span>, <span style="color: #666666">2</span>),
|
|
padding<span style="color: #666666">=</span><span style="color: #BA2121">'same'</span>))
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>LeakyReLU())
|
|
<span style="color: #408080; font-style: italic"># adding a dropout layer as you do in conv-nets</span>
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Dropout(<span style="color: #666666">0.3</span>))
|
|
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Flatten())
|
|
model<span style="color: #666666">.</span>add(layers<span style="color: #666666">.</span>Dense(<span style="color: #666666">1</span>))
|
|
|
|
<span style="color: #008000; font-weight: bold">return</span> model
|
|
</pre></div>
|
|
<p>
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<p>
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