added tensorflow
This commit is contained in:
mhjensen
@@ -140,7 +140,15 @@ div { text-align: justify; text-justify: inter-word; }
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None,
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'___sec47'),
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('scikit-learn implementation', 2, None, '___sec48'),
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('And then with Tensorflow', 2, None, '___sec49')]}
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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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end of tocinfo -->
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<body>
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@@ -2180,8 +2188,453 @@ plt<span style="color: #666666">.</span>show()
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="___sec49">And then with Tensorflow </h2>
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<h2 id="___sec49">Building neural networks in Tensorflow and Keras </h2>
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<p>
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Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn
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and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
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and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.
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<p>
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In our previous example we used only one hidden layer, and in this we will use two. From this it should be quite
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clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or
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NumPy arrays.
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="___sec50">Tensorflow </h2>
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<p>
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Tensorflow is an open source library machine learning library
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developed by the Google Brain team for internal use. It was released
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under the Apache 2.0 open source license in November 9, 2015.
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<p>
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Tensorflow is a computational framework that allows you to construct
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machine learning models at different levels of abstraction, from
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high-level, object-oriented APIs like Keras, down to the C++ kernels
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that Tensorflow is built upon. The higher levels of abstraction are
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simpler to use, but less flexible, and our choice of implementation
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should reflect the problems we are trying to solve.
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<p>
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<a href="https://www.tensorflow.org/guide/graphs" target="_blank">Tensorflow uses</a> so-called graphs to represent your computation
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in terms of the dependencies between individual operations, such that you first build a Tensorflow <em>graph</em>
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to represent your model, and then create a Tensorflow <em>session</em> to run the graph.
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<p>
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In this guide we will analyze the same data as we did in our NumPy and
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scikit-learn tutorial, gathered from the MNIST database of images. We
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will give an introduction to the lower level Python Application
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Program Interfaces (APIs), and see how we use them to build our graph.
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Then we will build (effectively) the same graph in Keras, to see just
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how simple solving a machine learning problem can be.
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<p>
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To install tensorflow on Unix/Linux systems, use pip as
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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>pip3 install tensorflow
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</pre></div>
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<p>
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and/or if you use <b>anaconda</b>, just write (or install from the graphical user interface)
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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>conda install tensorflow
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</pre></div>
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="___sec51">Collect and pre-process data </h2>
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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"># import necessary packages</span>
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<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
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<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> datasets
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<span style="color: #408080; font-style: italic"># ensure the same random numbers appear every time</span>
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np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">0</span>)
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<span style="color: #408080; font-style: italic"># display images in notebook</span>
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<span style="color: #666666">%</span>matplotlib inline
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plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'figure.figsize'</span>] <span style="color: #666666">=</span> (<span style="color: #666666">12</span>,<span style="color: #666666">12</span>)
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<span style="color: #408080; font-style: italic"># download MNIST dataset</span>
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digits <span style="color: #666666">=</span> datasets<span style="color: #666666">.</span>load_digits()
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<span style="color: #408080; font-style: italic"># define inputs and labels</span>
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inputs <span style="color: #666666">=</span> digits<span style="color: #666666">.</span>images
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labels <span style="color: #666666">=</span> digits<span style="color: #666666">.</span>target
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<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"inputs = (n_inputs, pixel_width, pixel_height) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(inputs<span style="color: #666666">.</span>shape))
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<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"labels = (n_inputs) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(labels<span style="color: #666666">.</span>shape))
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<span style="color: #408080; font-style: italic"># flatten the image</span>
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<span style="color: #408080; font-style: italic"># the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64</span>
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n_inputs <span style="color: #666666">=</span> <span style="color: #008000">len</span>(inputs)
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inputs <span style="color: #666666">=</span> inputs<span style="color: #666666">.</span>reshape(n_inputs, <span style="color: #666666">-1</span>)
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<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"X = (n_inputs, n_features) = "</span> <span style="color: #666666">+</span> <span style="color: #008000">str</span>(inputs<span style="color: #666666">.</span>shape))
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<span style="color: #408080; font-style: italic"># choose some random images to display</span>
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indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(n_inputs)
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random_indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>choice(indices, size<span style="color: #666666">=5</span>)
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<span style="color: #008000; font-weight: bold">for</span> i, image <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(digits<span style="color: #666666">.</span>images[random_indices]):
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plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">1</span>, <span style="color: #666666">5</span>, i<span style="color: #666666">+1</span>)
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plt<span style="color: #666666">.</span>axis(<span style="color: #BA2121">'off'</span>)
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plt<span style="color: #666666">.</span>imshow(image, cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>gray_r, interpolation<span style="color: #666666">=</span><span style="color: #BA2121">'nearest'</span>)
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plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">"Label: </span><span style="color: #BB6688; font-weight: bold">%d</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> digits<span style="color: #666666">.</span>target[random_indices[i]])
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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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<!-- 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">from</span> <span style="color: #0000FF; font-weight: bold">keras.utils</span> <span style="color: #008000; font-weight: bold">import</span> to_categorical
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
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<span style="color: #408080; font-style: italic"># one-hot representation of labels</span>
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labels <span style="color: #666666">=</span> to_categorical(labels)
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<span style="color: #408080; font-style: italic"># split into train and test data</span>
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train_size <span style="color: #666666">=</span> <span style="color: #666666">0.8</span>
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test_size <span style="color: #666666">=</span> <span style="color: #666666">1</span> <span style="color: #666666">-</span> train_size
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X_train, X_test, Y_train, Y_test <span style="color: #666666">=</span> train_test_split(inputs, labels, train_size<span style="color: #666666">=</span>train_size,
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test_size<span style="color: #666666">=</span>test_size)
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</pre></div>
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<p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="___sec52">Using TensorFlow backend </h2>
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<ol>
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<li> Define model and architecture</li>
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<li> Choose cost function and optimizer</li>
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</ol>
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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">import</span> <span style="color: #0000FF; font-weight: bold">tensorflow</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">tf</span>
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<span style="color: #008000; font-weight: bold">class</span> <span style="color: #0000FF; font-weight: bold">NeuralNetworkTensorflow</span>:
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">__init__</span>(
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<span style="color: #008000">self</span>,
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X_train,
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Y_train,
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X_test,
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Y_test,
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n_neurons_layer1<span style="color: #666666">=100</span>,
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n_neurons_layer2<span style="color: #666666">=50</span>,
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n_categories<span style="color: #666666">=2</span>,
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epochs<span style="color: #666666">=10</span>,
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batch_size<span style="color: #666666">=100</span>,
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eta<span style="color: #666666">=0.1</span>,
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lmbd<span style="color: #666666">=0.0</span>,
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):
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<span style="color: #408080; font-style: italic"># keep track of number of steps</span>
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<span style="color: #008000">self</span><span style="color: #666666">.</span>global_step <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>Variable(<span style="color: #666666">0</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>int32, trainable<span style="color: #666666">=</span><span style="color: #008000">False</span>, name<span style="color: #666666">=</span><span style="color: #BA2121">'global_step'</span>)
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<span style="color: #008000">self</span><span style="color: #666666">.</span>X_train <span style="color: #666666">=</span> X_train
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<span style="color: #008000">self</span><span style="color: #666666">.</span>Y_train <span style="color: #666666">=</span> Y_train
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<span style="color: #008000">self</span><span style="color: #666666">.</span>X_test <span style="color: #666666">=</span> X_test
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<span style="color: #008000">self</span><span style="color: #666666">.</span>Y_test <span style="color: #666666">=</span> Y_test
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<span style="color: #008000">self</span><span style="color: #666666">.</span>n_inputs <span style="color: #666666">=</span> X_train<span style="color: #666666">.</span>shape[<span style="color: #666666">0</span>]
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<span style="color: #008000">self</span><span style="color: #666666">.</span>n_features <span style="color: #666666">=</span> X_train<span style="color: #666666">.</span>shape[<span style="color: #666666">1</span>]
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<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1 <span style="color: #666666">=</span> n_neurons_layer1
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<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2 <span style="color: #666666">=</span> n_neurons_layer2
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<span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories <span style="color: #666666">=</span> n_categories
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<span style="color: #008000">self</span><span style="color: #666666">.</span>epochs <span style="color: #666666">=</span> epochs
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<span style="color: #008000">self</span><span style="color: #666666">.</span>batch_size <span style="color: #666666">=</span> batch_size
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<span style="color: #008000">self</span><span style="color: #666666">.</span>iterations <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>n_inputs <span style="color: #666666">//</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>batch_size
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<span style="color: #008000">self</span><span style="color: #666666">.</span>eta <span style="color: #666666">=</span> eta
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<span style="color: #008000">self</span><span style="color: #666666">.</span>lmbd <span style="color: #666666">=</span> lmbd
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<span style="color: #408080; font-style: italic"># build network piece by piece</span>
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<span style="color: #408080; font-style: italic"># name scopes (with) are used to enforce creation of new variables</span>
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<span style="color: #408080; font-style: italic"># https://www.tensorflow.org/guide/variables</span>
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<span style="color: #008000">self</span><span style="color: #666666">.</span>create_placeholders()
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<span style="color: #008000">self</span><span style="color: #666666">.</span>create_DNN()
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<span style="color: #008000">self</span><span style="color: #666666">.</span>create_loss()
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<span style="color: #008000">self</span><span style="color: #666666">.</span>create_optimiser()
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<span style="color: #008000">self</span><span style="color: #666666">.</span>create_accuracy()
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_placeholders</span>(<span style="color: #008000">self</span>):
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<span style="color: #408080; font-style: italic"># placeholders are fine here, but "Datasets" are the preferred method</span>
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<span style="color: #408080; font-style: italic"># of streaming data into a model</span>
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<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'data'</span>):
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<span style="color: #008000">self</span><span style="color: #666666">.</span>X <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>placeholder(tf<span style="color: #666666">.</span>float32, shape<span style="color: #666666">=</span>(<span style="color: #008000">None</span>, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_features), name<span style="color: #666666">=</span><span style="color: #BA2121">'X_data'</span>)
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<span style="color: #008000">self</span><span style="color: #666666">.</span>Y <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>placeholder(tf<span style="color: #666666">.</span>float32, shape<span style="color: #666666">=</span>(<span style="color: #008000">None</span>, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories), name<span style="color: #666666">=</span><span style="color: #BA2121">'Y_data'</span>)
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_DNN</span>(<span style="color: #008000">self</span>):
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<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'DNN'</span>):
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<span style="color: #408080; font-style: italic"># the weights are stored to calculate regularization loss later</span>
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<span style="color: #408080; font-style: italic"># Fully connected layer 1</span>
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<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc1 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>weight_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_features, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc1'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
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b_fc1 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>bias_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc1'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
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a_fc1 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>sigmoid(tf<span style="color: #666666">.</span>matmul(<span style="color: #008000">self</span><span style="color: #666666">.</span>X, <span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc1) <span style="color: #666666">+</span> b_fc1)
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<span style="color: #408080; font-style: italic"># Fully connected layer 2</span>
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<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc2 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>weight_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer1, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc2'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
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b_fc2 <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>bias_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2], name<span style="color: #666666">=</span><span style="color: #BA2121">'fc2'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
a_fc2 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>sigmoid(tf<span style="color: #666666">.</span>matmul(a_fc1, <span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc2) <span style="color: #666666">+</span> b_fc2)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Output layer</span>
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>W_out <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>weight_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_neurons_layer2, <span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories], name<span style="color: #666666">=</span><span style="color: #BA2121">'out'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
b_out <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>bias_variable([<span style="color: #008000">self</span><span style="color: #666666">.</span>n_categories], name<span style="color: #666666">=</span><span style="color: #BA2121">'out'</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>z_out <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>matmul(a_fc2, <span style="color: #008000">self</span><span style="color: #666666">.</span>W_out) <span style="color: #666666">+</span> b_out
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_loss</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'loss'</span>):
|
||||
softmax_loss <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>reduce_mean(tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>softmax_cross_entropy_with_logits_v2(labels<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>Y, logits<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>z_out))
|
||||
|
||||
regularizer_loss_fc1 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>l2_loss(<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc1)
|
||||
regularizer_loss_fc2 <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>l2_loss(<span style="color: #008000">self</span><span style="color: #666666">.</span>W_fc2)
|
||||
regularizer_loss_out <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>l2_loss(<span style="color: #008000">self</span><span style="color: #666666">.</span>W_out)
|
||||
regularizer_loss <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>lmbd<span style="color: #666666">*</span>(regularizer_loss_fc1 <span style="color: #666666">+</span> regularizer_loss_fc2 <span style="color: #666666">+</span> regularizer_loss_out)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>loss <span style="color: #666666">=</span> softmax_loss <span style="color: #666666">+</span> regularizer_loss
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_accuracy</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'accuracy'</span>):
|
||||
probabilities <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>nn<span style="color: #666666">.</span>softmax(<span style="color: #008000">self</span><span style="color: #666666">.</span>z_out)
|
||||
predictions <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>argmax(probabilities, axis<span style="color: #666666">=1</span>)
|
||||
labels <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>argmax(<span style="color: #008000">self</span><span style="color: #666666">.</span>Y, axis<span style="color: #666666">=1</span>)
|
||||
|
||||
correct_predictions <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>equal(predictions, labels)
|
||||
correct_predictions <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>cast(correct_predictions, tf<span style="color: #666666">.</span>float32)
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>accuracy <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>reduce_mean(correct_predictions)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_optimiser</span>(<span style="color: #008000">self</span>):
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>name_scope(<span style="color: #BA2121">'optimizer'</span>):
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>optimizer <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>train<span style="color: #666666">.</span>GradientDescentOptimizer(learning_rate<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>eta)<span style="color: #666666">.</span>minimize(<span style="color: #008000">self</span><span style="color: #666666">.</span>loss, global_step<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>global_step)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">weight_variable</span>(<span style="color: #008000">self</span>, shape, name<span style="color: #666666">=</span><span style="color: #BA2121">''</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32):
|
||||
initial <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>truncated_normal(shape, stddev<span style="color: #666666">=0.1</span>)
|
||||
<span style="color: #008000; font-weight: bold">return</span> tf<span style="color: #666666">.</span>Variable(initial, name<span style="color: #666666">=</span>name, dtype<span style="color: #666666">=</span>dtype)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">bias_variable</span>(<span style="color: #008000">self</span>, shape, name<span style="color: #666666">=</span><span style="color: #BA2121">''</span>, dtype<span style="color: #666666">=</span>tf<span style="color: #666666">.</span>float32):
|
||||
initial <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>constant(<span style="color: #666666">0.1</span>, shape<span style="color: #666666">=</span>shape)
|
||||
<span style="color: #008000; font-weight: bold">return</span> tf<span style="color: #666666">.</span>Variable(initial, name<span style="color: #666666">=</span>name, dtype<span style="color: #666666">=</span>dtype)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">fit</span>(<span style="color: #008000">self</span>):
|
||||
data_indices <span style="color: #666666">=</span> np<span style="color: #666666">.</span>arange(<span style="color: #008000">self</span><span style="color: #666666">.</span>n_inputs)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">with</span> tf<span style="color: #666666">.</span>Session() <span style="color: #008000; font-weight: bold">as</span> sess:
|
||||
sess<span style="color: #666666">.</span>run(tf<span style="color: #666666">.</span>global_variables_initializer())
|
||||
<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">self</span><span style="color: #666666">.</span>epochs):
|
||||
<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">self</span><span style="color: #666666">.</span>iterations):
|
||||
chosen_datapoints <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>choice(data_indices, size<span style="color: #666666">=</span><span style="color: #008000">self</span><span style="color: #666666">.</span>batch_size, replace<span style="color: #666666">=</span><span style="color: #008000">False</span>)
|
||||
batch_X, batch_Y <span style="color: #666666">=</span> <span style="color: #008000">self</span><span style="color: #666666">.</span>X_train[chosen_datapoints], <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_train[chosen_datapoints]
|
||||
|
||||
sess<span style="color: #666666">.</span>run([DNN<span style="color: #666666">.</span>loss, DNN<span style="color: #666666">.</span>optimizer],
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: batch_X,
|
||||
DNN<span style="color: #666666">.</span>Y: batch_Y})
|
||||
accuracy <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run(DNN<span style="color: #666666">.</span>accuracy,
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: batch_X,
|
||||
DNN<span style="color: #666666">.</span>Y: batch_Y})
|
||||
step <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run(DNN<span style="color: #666666">.</span>global_step)
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>train_loss, <span style="color: #008000">self</span><span style="color: #666666">.</span>train_accuracy <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run([DNN<span style="color: #666666">.</span>loss, DNN<span style="color: #666666">.</span>accuracy],
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: <span style="color: #008000">self</span><span style="color: #666666">.</span>X_train,
|
||||
DNN<span style="color: #666666">.</span>Y: <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_train})
|
||||
|
||||
<span style="color: #008000">self</span><span style="color: #666666">.</span>test_loss, <span style="color: #008000">self</span><span style="color: #666666">.</span>test_accuracy <span style="color: #666666">=</span> sess<span style="color: #666666">.</span>run([DNN<span style="color: #666666">.</span>loss, DNN<span style="color: #666666">.</span>accuracy],
|
||||
feed_dict<span style="color: #666666">=</span>{DNN<span style="color: #666666">.</span>X: <span style="color: #008000">self</span><span style="color: #666666">.</span>X_test,
|
||||
DNN<span style="color: #666666">.</span>Y: <span style="color: #008000">self</span><span style="color: #666666">.</span>Y_test})
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec53">Optimizing and using gradient descent </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>epochs <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
batch_size <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
n_neurons_layer1 <span style="color: #666666">=</span> <span style="color: #666666">100</span>
|
||||
n_neurons_layer2 <span style="color: #666666">=</span> <span style="color: #666666">50</span>
|
||||
n_categories <span style="color: #666666">=</span> <span style="color: #666666">10</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>)
|
||||
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>)
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>DNN_tf <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>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i, eta <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(eta_vals):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j, lmbd <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(lmbd_vals):
|
||||
DNN <span style="color: #666666">=</span> NeuralNetworkTensorflow(X_train, Y_train, X_test, Y_test,
|
||||
n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
epochs<span style="color: #666666">=</span>epochs, batch_size<span style="color: #666666">=</span>batch_size, eta<span style="color: #666666">=</span>eta, lmbd<span style="color: #666666">=</span>lmbd)
|
||||
DNN<span style="color: #666666">.</span>fit()
|
||||
|
||||
DNN_tf[i][j] <span style="color: #666666">=</span> DNN
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Learning rate = "</span>, eta)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Test accuracy: </span><span style="color: #BB6688; font-weight: bold">%.3f</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> DNN<span style="color: #666666">.</span>test_accuracy)
|
||||
<span style="color: #008000; font-weight: bold">print</span>()
|
||||
|
||||
</pre></div>
|
||||
<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: #408080; font-style: italic"># optional</span>
|
||||
<span style="color: #408080; font-style: italic"># visual representation of grid search</span>
|
||||
<span style="color: #408080; font-style: italic"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<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>
|
||||
|
||||
sns<span style="color: #666666">.</span>set()
|
||||
|
||||
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)))
|
||||
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)))
|
||||
|
||||
<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)):
|
||||
<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)):
|
||||
DNN <span style="color: #666666">=</span> DNN_tf[i][j]
|
||||
|
||||
train_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>train_accuracy
|
||||
test_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>test_accuracy
|
||||
|
||||
|
||||
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>))
|
||||
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>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Training Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
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>))
|
||||
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>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Test Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<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: #408080; font-style: italic"># optional</span>
|
||||
<span style="color: #408080; font-style: italic"># we can use log files to visualize our graph in Tensorboard</span>
|
||||
writer <span style="color: #666666">=</span> tf<span style="color: #666666">.</span>summary<span style="color: #666666">.</span>FileWriter(<span style="color: #BA2121">'logs/'</span>)
|
||||
writer<span style="color: #666666">.</span>add_graph(tf<span style="color: #666666">.</span>get_default_graph())
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec54">Using Keras </h2>
|
||||
|
||||
<p>
|
||||
Keras is a high level <a href="https://en.wikipedia.org/wiki/Application_programming_interface" target="_blank">neural network</a>
|
||||
that supports Tensorflow, CTNK and Theano as backends.
|
||||
If you have Tensorflow installed Keras is available through the <em>tf.keras</em> module.
|
||||
If you have Anaconda installed you may run the following command
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>conda install keras
|
||||
</pre></div>
|
||||
<p>
|
||||
Alternatively, if you have Tensorflow or one of the other supported backends install you may use the pip package manager:
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pip3 install keras
|
||||
</pre></div>
|
||||
<p>
|
||||
or look up the <a href="https://keras.io/" target="_blank">instructions here</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">from</span> <span style="color: #0000FF; font-weight: bold">keras.models</span> <span style="color: #008000; font-weight: bold">import</span> Sequential
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.layers</span> <span style="color: #008000; font-weight: bold">import</span> Dense
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.regularizers</span> <span style="color: #008000; font-weight: bold">import</span> l2
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">keras.optimizers</span> <span style="color: #008000; font-weight: bold">import</span> SGD
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">create_neural_network_keras</span>(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
|
||||
model <span style="color: #666666">=</span> Sequential()
|
||||
model<span style="color: #666666">.</span>add(Dense(n_neurons_layer1, activation<span style="color: #666666">=</span><span style="color: #BA2121">'sigmoid'</span>, kernel_regularizer<span style="color: #666666">=</span>l2(lmbd)))
|
||||
model<span style="color: #666666">.</span>add(Dense(n_neurons_layer2, activation<span style="color: #666666">=</span><span style="color: #BA2121">'sigmoid'</span>, kernel_regularizer<span style="color: #666666">=</span>l2(lmbd)))
|
||||
model<span style="color: #666666">.</span>add(Dense(n_categories, activation<span style="color: #666666">=</span><span style="color: #BA2121">'softmax'</span>))
|
||||
|
||||
sgd <span style="color: #666666">=</span> SGD(lr<span style="color: #666666">=</span>eta)
|
||||
model<span style="color: #666666">.</span>compile(loss<span style="color: #666666">=</span><span style="color: #BA2121">'categorical_crossentropy'</span>, optimizer<span style="color: #666666">=</span>sgd, metrics<span style="color: #666666">=</span>[<span style="color: #BA2121">'accuracy'</span>])
|
||||
|
||||
<span style="color: #008000; font-weight: bold">return</span> model
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>DNN_keras <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>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i, eta <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(eta_vals):
|
||||
<span style="color: #008000; font-weight: bold">for</span> j, lmbd <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(lmbd_vals):
|
||||
DNN <span style="color: #666666">=</span> create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
eta<span style="color: #666666">=</span>eta, lmbd<span style="color: #666666">=</span>lmbd)
|
||||
DNN<span style="color: #666666">.</span>fit(X_train, Y_train, epochs<span style="color: #666666">=</span>epochs, batch_size<span style="color: #666666">=</span>batch_size, verbose<span style="color: #666666">=0</span>)
|
||||
scores <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>evaluate(X_test, Y_test)
|
||||
|
||||
DNN_keras[i][j] <span style="color: #666666">=</span> DNN
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Learning rate = "</span>, eta)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Test accuracy: </span><span style="color: #BB6688; font-weight: bold">%.3f</span><span style="color: #BA2121">"</span> <span style="color: #666666">%</span> scores[<span style="color: #666666">1</span>])
|
||||
<span style="color: #008000; font-weight: bold">print</span>()
|
||||
</pre></div>
|
||||
<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: #408080; font-style: italic"># optional</span>
|
||||
<span style="color: #408080; font-style: italic"># visual representation of grid search</span>
|
||||
<span style="color: #408080; font-style: italic"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<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>
|
||||
|
||||
sns<span style="color: #666666">.</span>set()
|
||||
|
||||
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)))
|
||||
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)))
|
||||
|
||||
<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)):
|
||||
<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)):
|
||||
DNN <span style="color: #666666">=</span> DNN_keras[i][j]
|
||||
|
||||
train_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>evaluate(X_train, Y_train)[<span style="color: #666666">1</span>]
|
||||
test_accuracy[i][j] <span style="color: #666666">=</span> DNN<span style="color: #666666">.</span>evaluate(X_test, Y_test)[<span style="color: #666666">1</span>]
|
||||
|
||||
|
||||
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>))
|
||||
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>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Training Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
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>))
|
||||
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>)
|
||||
ax<span style="color: #666666">.</span>set_title(<span style="color: #BA2121">"Test Accuracy"</span>)
|
||||
ax<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"$\eta$"</span>)
|
||||
ax<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"$\lambda$"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
Reference in New Issue
Block a user