added tensorflow
This commit is contained in:
mhjensen
@@ -135,7 +135,15 @@ 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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@@ -2175,8 +2183,453 @@ plt.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 "perldoc" -->
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<div class="highlight" style="background: #eeeedd"><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 "perldoc" -->
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<div class="highlight" style="background: #eeeedd"><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 "perldoc" -->
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<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># import necessary packages</span>
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
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<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn</span> <span style="color: #8B008B; font-weight: bold">import</span> datasets
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<span style="color: #228B22"># ensure the same random numbers appear every time</span>
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np.random.seed(<span style="color: #B452CD">0</span>)
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<span style="color: #228B22"># display images in notebook</span>
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%matplotlib inline
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plt.rcParams[<span style="color: #CD5555">'figure.figsize'</span>] = (<span style="color: #B452CD">12</span>,<span style="color: #B452CD">12</span>)
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<span style="color: #228B22"># download MNIST dataset</span>
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digits = datasets.load_digits()
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<span style="color: #228B22"># define inputs and labels</span>
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inputs = digits.images
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labels = digits.target
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<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"inputs = (n_inputs, pixel_width, pixel_height) = "</span> + <span style="color: #658b00">str</span>(inputs.shape))
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<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"labels = (n_inputs) = "</span> + <span style="color: #658b00">str</span>(labels.shape))
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<span style="color: #228B22"># flatten the image</span>
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<span style="color: #228B22"># the value -1 means dimension is inferred from the remaining dimensions: 8x8 = 64</span>
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n_inputs = <span style="color: #658b00">len</span>(inputs)
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inputs = inputs.reshape(n_inputs, -<span style="color: #B452CD">1</span>)
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<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"X = (n_inputs, n_features) = "</span> + <span style="color: #658b00">str</span>(inputs.shape))
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<span style="color: #228B22"># choose some random images to display</span>
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indices = np.arange(n_inputs)
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random_indices = np.random.choice(indices, size=<span style="color: #B452CD">5</span>)
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<span style="color: #8B008B; font-weight: bold">for</span> i, image <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(digits.images[random_indices]):
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plt.subplot(<span style="color: #B452CD">1</span>, <span style="color: #B452CD">5</span>, i+<span style="color: #B452CD">1</span>)
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plt.axis(<span style="color: #CD5555">'off'</span>)
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plt.imshow(image, cmap=plt.cm.gray_r, interpolation=<span style="color: #CD5555">'nearest'</span>)
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plt.title(<span style="color: #CD5555">"Label: %d"</span> % digits.target[random_indices[i]])
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plt.show()
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</pre></div>
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<p>
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<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
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<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.utils</span> <span style="color: #8B008B; font-weight: bold">import</span> to_categorical
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<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> train_test_split
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<span style="color: #228B22"># one-hot representation of labels</span>
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labels = to_categorical(labels)
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<span style="color: #228B22"># split into train and test data</span>
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train_size = <span style="color: #B452CD">0.8</span>
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test_size = <span style="color: #B452CD">1</span> - train_size
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X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
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test_size=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 "perldoc" -->
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<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">tensorflow</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">tf</span>
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<span style="color: #8B008B; font-weight: bold">class</span> <span style="color: #008b45; font-weight: bold">NeuralNetworkTensorflow</span>:
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">__init__</span>(
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<span style="color: #658b00">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: #B452CD">100</span>,
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n_neurons_layer2=<span style="color: #B452CD">50</span>,
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n_categories=<span style="color: #B452CD">2</span>,
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epochs=<span style="color: #B452CD">10</span>,
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batch_size=<span style="color: #B452CD">100</span>,
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eta=<span style="color: #B452CD">0.1</span>,
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lmbd=<span style="color: #B452CD">0.0</span>,
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):
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<span style="color: #228B22"># keep track of number of steps</span>
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<span style="color: #658b00">self</span>.global_step = tf.Variable(<span style="color: #B452CD">0</span>, dtype=tf.int32, trainable=<span style="color: #658b00">False</span>, name=<span style="color: #CD5555">'global_step'</span>)
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<span style="color: #658b00">self</span>.X_train = X_train
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<span style="color: #658b00">self</span>.Y_train = Y_train
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<span style="color: #658b00">self</span>.X_test = X_test
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<span style="color: #658b00">self</span>.Y_test = Y_test
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<span style="color: #658b00">self</span>.n_inputs = X_train.shape[<span style="color: #B452CD">0</span>]
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<span style="color: #658b00">self</span>.n_features = X_train.shape[<span style="color: #B452CD">1</span>]
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<span style="color: #658b00">self</span>.n_neurons_layer1 = n_neurons_layer1
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<span style="color: #658b00">self</span>.n_neurons_layer2 = n_neurons_layer2
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<span style="color: #658b00">self</span>.n_categories = n_categories
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<span style="color: #658b00">self</span>.epochs = epochs
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<span style="color: #658b00">self</span>.batch_size = batch_size
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<span style="color: #658b00">self</span>.iterations = <span style="color: #658b00">self</span>.n_inputs // <span style="color: #658b00">self</span>.batch_size
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<span style="color: #658b00">self</span>.eta = eta
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<span style="color: #658b00">self</span>.lmbd = lmbd
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<span style="color: #228B22"># build network piece by piece</span>
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<span style="color: #228B22"># name scopes (with) are used to enforce creation of new variables</span>
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<span style="color: #228B22"># https://www.tensorflow.org/guide/variables</span>
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<span style="color: #658b00">self</span>.create_placeholders()
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<span style="color: #658b00">self</span>.create_DNN()
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<span style="color: #658b00">self</span>.create_loss()
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<span style="color: #658b00">self</span>.create_optimiser()
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<span style="color: #658b00">self</span>.create_accuracy()
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_placeholders</span>(<span style="color: #658b00">self</span>):
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<span style="color: #228B22"># placeholders are fine here, but "Datasets" are the preferred method</span>
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<span style="color: #228B22"># of streaming data into a model</span>
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<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'data'</span>):
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<span style="color: #658b00">self</span>.X = tf.placeholder(tf.float32, shape=(<span style="color: #658b00">None</span>, <span style="color: #658b00">self</span>.n_features), name=<span style="color: #CD5555">'X_data'</span>)
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<span style="color: #658b00">self</span>.Y = tf.placeholder(tf.float32, shape=(<span style="color: #658b00">None</span>, <span style="color: #658b00">self</span>.n_categories), name=<span style="color: #CD5555">'Y_data'</span>)
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_DNN</span>(<span style="color: #658b00">self</span>):
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<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'DNN'</span>):
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<span style="color: #228B22"># the weights are stored to calculate regularization loss later</span>
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<span style="color: #228B22"># Fully connected layer 1</span>
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<span style="color: #658b00">self</span>.W_fc1 = <span style="color: #658b00">self</span>.weight_variable([<span style="color: #658b00">self</span>.n_features, <span style="color: #658b00">self</span>.n_neurons_layer1], name=<span style="color: #CD5555">'fc1'</span>, dtype=tf.float32)
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b_fc1 = <span style="color: #658b00">self</span>.bias_variable([<span style="color: #658b00">self</span>.n_neurons_layer1], name=<span style="color: #CD5555">'fc1'</span>, dtype=tf.float32)
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a_fc1 = tf.nn.sigmoid(tf.matmul(<span style="color: #658b00">self</span>.X, <span style="color: #658b00">self</span>.W_fc1) + b_fc1)
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<span style="color: #228B22"># Fully connected layer 2</span>
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<span style="color: #658b00">self</span>.W_fc2 = <span style="color: #658b00">self</span>.weight_variable([<span style="color: #658b00">self</span>.n_neurons_layer1, <span style="color: #658b00">self</span>.n_neurons_layer2], name=<span style="color: #CD5555">'fc2'</span>, dtype=tf.float32)
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b_fc2 = <span style="color: #658b00">self</span>.bias_variable([<span style="color: #658b00">self</span>.n_neurons_layer2], name=<span style="color: #CD5555">'fc2'</span>, dtype=tf.float32)
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a_fc2 = tf.nn.sigmoid(tf.matmul(a_fc1, <span style="color: #658b00">self</span>.W_fc2) + b_fc2)
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<span style="color: #228B22"># Output layer</span>
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<span style="color: #658b00">self</span>.W_out = <span style="color: #658b00">self</span>.weight_variable([<span style="color: #658b00">self</span>.n_neurons_layer2, <span style="color: #658b00">self</span>.n_categories], name=<span style="color: #CD5555">'out'</span>, dtype=tf.float32)
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b_out = <span style="color: #658b00">self</span>.bias_variable([<span style="color: #658b00">self</span>.n_categories], name=<span style="color: #CD5555">'out'</span>, dtype=tf.float32)
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<span style="color: #658b00">self</span>.z_out = tf.matmul(a_fc2, <span style="color: #658b00">self</span>.W_out) + b_out
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_loss</span>(<span style="color: #658b00">self</span>):
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<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'loss'</span>):
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softmax_loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits_v2(labels=<span style="color: #658b00">self</span>.Y, logits=<span style="color: #658b00">self</span>.z_out))
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regularizer_loss_fc1 = tf.nn.l2_loss(<span style="color: #658b00">self</span>.W_fc1)
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regularizer_loss_fc2 = tf.nn.l2_loss(<span style="color: #658b00">self</span>.W_fc2)
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regularizer_loss_out = tf.nn.l2_loss(<span style="color: #658b00">self</span>.W_out)
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regularizer_loss = <span style="color: #658b00">self</span>.lmbd*(regularizer_loss_fc1 + regularizer_loss_fc2 + regularizer_loss_out)
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<span style="color: #658b00">self</span>.loss = softmax_loss + regularizer_loss
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_accuracy</span>(<span style="color: #658b00">self</span>):
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<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'accuracy'</span>):
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probabilities = tf.nn.softmax(<span style="color: #658b00">self</span>.z_out)
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predictions = tf.argmax(probabilities, axis=<span style="color: #B452CD">1</span>)
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labels = tf.argmax(<span style="color: #658b00">self</span>.Y, axis=<span style="color: #B452CD">1</span>)
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correct_predictions = tf.equal(predictions, labels)
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correct_predictions = tf.cast(correct_predictions, tf.float32)
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<span style="color: #658b00">self</span>.accuracy = tf.reduce_mean(correct_predictions)
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_optimiser</span>(<span style="color: #658b00">self</span>):
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<span style="color: #8B008B; font-weight: bold">with</span> tf.name_scope(<span style="color: #CD5555">'optimizer'</span>):
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<span style="color: #658b00">self</span>.optimizer = tf.train.GradientDescentOptimizer(learning_rate=<span style="color: #658b00">self</span>.eta).minimize(<span style="color: #658b00">self</span>.loss, global_step=<span style="color: #658b00">self</span>.global_step)
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">weight_variable</span>(<span style="color: #658b00">self</span>, shape, name=<span style="color: #CD5555">''</span>, dtype=tf.float32):
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initial = tf.truncated_normal(shape, stddev=<span style="color: #B452CD">0.1</span>)
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<span style="color: #8B008B; font-weight: bold">return</span> tf.Variable(initial, name=name, dtype=dtype)
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">bias_variable</span>(<span style="color: #658b00">self</span>, shape, name=<span style="color: #CD5555">''</span>, dtype=tf.float32):
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initial = tf.constant(<span style="color: #B452CD">0.1</span>, shape=shape)
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<span style="color: #8B008B; font-weight: bold">return</span> tf.Variable(initial, name=name, dtype=dtype)
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<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">fit</span>(<span style="color: #658b00">self</span>):
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data_indices = np.arange(<span style="color: #658b00">self</span>.n_inputs)
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|
||||
<span style="color: #8B008B; font-weight: bold">with</span> tf.Session() <span style="color: #8B008B; font-weight: bold">as</span> sess:
|
||||
sess.run(tf.global_variables_initializer())
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">self</span>.epochs):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">self</span>.iterations):
|
||||
chosen_datapoints = np.random.choice(data_indices, size=<span style="color: #658b00">self</span>.batch_size, replace=<span style="color: #658b00">False</span>)
|
||||
batch_X, batch_Y = <span style="color: #658b00">self</span>.X_train[chosen_datapoints], <span style="color: #658b00">self</span>.Y_train[chosen_datapoints]
|
||||
|
||||
sess.run([DNN.loss, DNN.optimizer],
|
||||
feed_dict={DNN.X: batch_X,
|
||||
DNN.Y: batch_Y})
|
||||
accuracy = sess.run(DNN.accuracy,
|
||||
feed_dict={DNN.X: batch_X,
|
||||
DNN.Y: batch_Y})
|
||||
step = sess.run(DNN.global_step)
|
||||
|
||||
<span style="color: #658b00">self</span>.train_loss, <span style="color: #658b00">self</span>.train_accuracy = sess.run([DNN.loss, DNN.accuracy],
|
||||
feed_dict={DNN.X: <span style="color: #658b00">self</span>.X_train,
|
||||
DNN.Y: <span style="color: #658b00">self</span>.Y_train})
|
||||
|
||||
<span style="color: #658b00">self</span>.test_loss, <span style="color: #658b00">self</span>.test_accuracy = sess.run([DNN.loss, DNN.accuracy],
|
||||
feed_dict={DNN.X: <span style="color: #658b00">self</span>.X_test,
|
||||
DNN.Y: <span style="color: #658b00">self</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 "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>epochs = <span style="color: #B452CD">100</span>
|
||||
batch_size = <span style="color: #B452CD">100</span>
|
||||
n_neurons_layer1 = <span style="color: #B452CD">100</span>
|
||||
n_neurons_layer2 = <span style="color: #B452CD">50</span>
|
||||
n_categories = <span style="color: #B452CD">10</span>
|
||||
|
||||
eta_vals = np.logspace(-<span style="color: #B452CD">5</span>, <span style="color: #B452CD">1</span>, <span style="color: #B452CD">7</span>)
|
||||
lmbd_vals = np.logspace(-<span style="color: #B452CD">5</span>, <span style="color: #B452CD">1</span>, <span style="color: #B452CD">7</span>)
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>DNN_tf = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)), dtype=<span style="color: #658b00">object</span>)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i, eta <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(eta_vals):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j, lmbd <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(lmbd_vals):
|
||||
DNN = NeuralNetworkTensorflow(X_train, Y_train, X_test, Y_test,
|
||||
n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
epochs=epochs, batch_size=batch_size, eta=eta, lmbd=lmbd)
|
||||
DNN.fit()
|
||||
|
||||
DNN_tf[i][j] = DNN
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Learning rate = "</span>, eta)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Test accuracy: %.3f"</span> % DNN.test_accuracy)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>()
|
||||
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># optional</span>
|
||||
<span style="color: #228B22"># visual representation of grid search</span>
|
||||
<span style="color: #228B22"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
|
||||
|
||||
sns.set()
|
||||
|
||||
train_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
test_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(eta_vals)):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(lmbd_vals)):
|
||||
DNN = DNN_tf[i][j]
|
||||
|
||||
train_accuracy[i][j] = DNN.train_accuracy
|
||||
test_accuracy[i][j] = DNN.test_accuracy
|
||||
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(train_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Training Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(test_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Test Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># optional</span>
|
||||
<span style="color: #228B22"># we can use log files to visualize our graph in Tensorboard</span>
|
||||
writer = tf.summary.FileWriter(<span style="color: #CD5555">'logs/'</span>)
|
||||
writer.add_graph(tf.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 "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><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 "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><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 "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.models</span> <span style="color: #8B008B; font-weight: bold">import</span> Sequential
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.layers</span> <span style="color: #8B008B; font-weight: bold">import</span> Dense
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.regularizers</span> <span style="color: #8B008B; font-weight: bold">import</span> l2
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">keras.optimizers</span> <span style="color: #8B008B; font-weight: bold">import</span> SGD
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">create_neural_network_keras</span>(n_neurons_layer1, n_neurons_layer2, n_categories, eta, lmbd):
|
||||
model = Sequential()
|
||||
model.add(Dense(n_neurons_layer1, activation=<span style="color: #CD5555">'sigmoid'</span>, kernel_regularizer=l2(lmbd)))
|
||||
model.add(Dense(n_neurons_layer2, activation=<span style="color: #CD5555">'sigmoid'</span>, kernel_regularizer=l2(lmbd)))
|
||||
model.add(Dense(n_categories, activation=<span style="color: #CD5555">'softmax'</span>))
|
||||
|
||||
sgd = SGD(lr=eta)
|
||||
model.compile(loss=<span style="color: #CD5555">'categorical_crossentropy'</span>, optimizer=sgd, metrics=[<span style="color: #CD5555">'accuracy'</span>])
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">return</span> model
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span>DNN_keras = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)), dtype=<span style="color: #658b00">object</span>)
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i, eta <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(eta_vals):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j, lmbd <span style="color: #8B008B">in</span> <span style="color: #658b00">enumerate</span>(lmbd_vals):
|
||||
DNN = create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories,
|
||||
eta=eta, lmbd=lmbd)
|
||||
DNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=<span style="color: #B452CD">0</span>)
|
||||
scores = DNN.evaluate(X_test, Y_test)
|
||||
|
||||
DNN_keras[i][j] = DNN
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Learning rate = "</span>, eta)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Lambda = "</span>, lmbd)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Test accuracy: %.3f"</span> % scores[<span style="color: #B452CD">1</span>])
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #228B22"># optional</span>
|
||||
<span style="color: #228B22"># visual representation of grid search</span>
|
||||
<span style="color: #228B22"># uses seaborn heatmap, could probably do this in matplotlib</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
|
||||
|
||||
sns.set()
|
||||
|
||||
train_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
test_accuracy = np.zeros((<span style="color: #658b00">len</span>(eta_vals), <span style="color: #658b00">len</span>(lmbd_vals)))
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(eta_vals)):
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> j <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #658b00">len</span>(lmbd_vals)):
|
||||
DNN = DNN_keras[i][j]
|
||||
|
||||
train_accuracy[i][j] = DNN.evaluate(X_train, Y_train)[<span style="color: #B452CD">1</span>]
|
||||
test_accuracy[i][j] = DNN.evaluate(X_test, Y_test)[<span style="color: #B452CD">1</span>]
|
||||
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(train_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Training Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
|
||||
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
|
||||
sns.heatmap(test_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">"viridis"</span>)
|
||||
ax.set_title(<span style="color: #CD5555">"Test Accuracy"</span>)
|
||||
ax.set_ylabel(<span style="color: #CD5555">"$\eta$"</span>)
|
||||
ax.set_xlabel(<span style="color: #CD5555">"$\lambda$"</span>)
|
||||
plt.show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
Reference in New Issue
Block a user