Updating slides
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mhjensen
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# import necessary packages
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import numpy as np
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import matplotlib.pyplot as plt
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from sklearn import datasets
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# ensure the same random numbers appear every time
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np.random.seed(0)
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# display images in notebook
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plt.rcParams['figure.figsize'] = (12,12)
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# download MNIST dataset
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digits = datasets.load_digits()
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# define inputs and labels
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inputs = digits.images
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labels = digits.target
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# RGB images have a depth of 3
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# our images are grayscale so they should have a depth of 1
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inputs = inputs[:,:,:,np.newaxis]
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print("inputs = (n_inputs, pixel_width, pixel_height, depth) = " + str(inputs.shape))
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print("labels = (n_inputs) = " + str(labels.shape))
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# choose some random images to display
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n_inputs = len(inputs)
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indices = np.arange(n_inputs)
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random_indices = np.random.choice(indices, size=5)
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for i, image in enumerate(digits.images[random_indices]):
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plt.subplot(1, 5, i+1)
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plt.axis('off')
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plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
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plt.title("Label: %d" % digits.target[random_indices[i]])
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plt.show()
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from keras.utils import to_categorical
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from sklearn.model_selection import train_test_split
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# representation of labels
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labels = to_categorical(labels)
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# split into train and test data
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# one-liner from scikit-learn library
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train_size = 0.8
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test_size = 1 - 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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import tensorflow as tf
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class ConvolutionalNeuralNetworkTensorflow:
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def __init__(
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self,
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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_filters=10,
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n_neurons_connected=50,
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n_categories=10,
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receptive_field=3,
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stride=1,
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padding=1,
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epochs=10,
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batch_size=100,
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eta=0.1,
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lmbd=0.0,
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):
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self.global_step = tf.Variable(0, dtype=tf.int32, trainable=False, name='global_step')
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self.X_train = X_train
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self.Y_train = Y_train
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self.X_test = X_test
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self.Y_test = Y_test
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self.n_inputs, self.input_width, self.input_height, self.depth = X_train.shape
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self.n_filters = n_filters
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self.n_downsampled = int(self.input_width*self.input_height*n_filters / 4)
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self.n_neurons_connected = n_neurons_connected
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self.n_categories = n_categories
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self.receptive_field = receptive_field
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self.stride = stride
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self.strides = [stride, stride, stride, stride]
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self.padding = padding
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self.epochs = epochs
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self.batch_size = batch_size
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self.iterations = self.n_inputs // self.batch_size
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self.eta = eta
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self.lmbd = lmbd
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self.create_placeholders()
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self.create_CNN()
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self.create_loss()
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self.create_optimiser()
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self.create_accuracy()
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def create_placeholders(self):
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with tf.name_scope('data'):
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self.X = tf.placeholder(tf.float32, shape=(None, self.input_width, self.input_height, self.depth), name='X_data')
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self.Y = tf.placeholder(tf.float32, shape=(None, self.n_categories), name='Y_data')
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def create_CNN(self):
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with tf.name_scope('CNN'):
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# Convolutional layer
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self.W_conv = self.weight_variable([self.receptive_field, self.receptive_field, self.depth, self.n_filters], name='conv', dtype=tf.float32)
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b_conv = self.weight_variable([self.n_filters], name='conv', dtype=tf.float32)
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z_conv = tf.nn.conv2d(self.X, self.W_conv, self.strides, padding='SAME', name='conv') + b_conv
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a_conv = tf.nn.relu(z_conv)
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# 2x2 max pooling
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a_pool = tf.nn.max_pool(a_conv, [1, 2, 2, 1], [1, 2, 2, 1], padding='SAME', name='pool')
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# Fully connected layer
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a_pool_flat = tf.reshape(a_pool, [-1, self.n_downsampled])
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self.W_fc = self.weight_variable([self.n_downsampled, self.n_neurons_connected], name='fc', dtype=tf.float32)
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b_fc = self.bias_variable([self.n_neurons_connected], name='fc', dtype=tf.float32)
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a_fc = tf.nn.relu(tf.matmul(a_pool_flat, self.W_fc) + b_fc)
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# Output layer
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self.W_out = self.weight_variable([self.n_neurons_connected, self.n_categories], name='out', dtype=tf.float32)
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b_out = self.bias_variable([self.n_categories], name='out', dtype=tf.float32)
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self.z_out = tf.matmul(a_fc, self.W_out) + b_out
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def create_loss(self):
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with tf.name_scope('loss'):
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softmax_loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits_v2(labels=self.Y, logits=self.z_out))
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regularizer_loss_conv = tf.nn.l2_loss(self.W_conv)
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regularizer_loss_fc = tf.nn.l2_loss(self.W_fc)
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regularizer_loss_out = tf.nn.l2_loss(self.W_out)
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regularizer_loss = self.lmbd*(regularizer_loss_conv + regularizer_loss_fc + regularizer_loss_out)
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self.loss = softmax_loss + regularizer_loss
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def create_accuracy(self):
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with tf.name_scope('accuracy'):
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probabilities = tf.nn.softmax(self.z_out)
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predictions = tf.argmax(probabilities, 1)
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labels = tf.argmax(self.Y, 1)
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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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self.accuracy = tf.reduce_mean(correct_predictions)
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def create_optimiser(self):
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with tf.name_scope('optimizer'):
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self.optimizer = tf.train.GradientDescentOptimizer(learning_rate=self.eta).minimize(self.loss, global_step=self.global_step)
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def weight_variable(self, shape, name='', dtype=tf.float32):
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initial = tf.truncated_normal(shape, stddev=0.1)
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return tf.Variable(initial, name=name, dtype=dtype)
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def bias_variable(self, shape, name='', dtype=tf.float32):
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initial = tf.constant(0.1, shape=shape)
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return tf.Variable(initial, name=name, dtype=dtype)
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def fit(self):
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data_indices = np.arange(self.n_inputs)
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with tf.Session() as sess:
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sess.run(tf.global_variables_initializer())
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for i in range(self.epochs):
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for j in range(self.iterations):
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chosen_datapoints = np.random.choice(data_indices, size=self.batch_size, replace=False)
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batch_X, batch_Y = self.X_train[chosen_datapoints], self.Y_train[chosen_datapoints]
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sess.run([CNN.loss, CNN.optimizer],
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feed_dict={CNN.X: batch_X,
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CNN.Y: batch_Y})
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accuracy = sess.run(CNN.accuracy,
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feed_dict={CNN.X: batch_X,
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CNN.Y: batch_Y})
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step = sess.run(CNN.global_step)
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self.train_loss, self.train_accuracy = sess.run([CNN.loss, CNN.accuracy],
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feed_dict={CNN.X: self.X_train,
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CNN.Y: self.Y_train})
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self.test_loss, self.test_accuracy = sess.run([CNN.loss, CNN.accuracy],
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feed_dict={CNN.X: self.X_test,
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CNN.Y: self.Y_test})
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epochs = 100
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batch_size = 100
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n_filters = 10
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n_neurons_connected = 50
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n_categories = 10
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eta_vals = np.logspace(-5, 1, 7)
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lmbd_vals = np.logspace(-5, 1, 7)
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CNN_tf = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
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for i, eta in enumerate(eta_vals):
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for j, lmbd in enumerate(lmbd_vals):
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CNN = ConvolutionalNeuralNetworkTensorflow(X_train, Y_train, X_test, Y_test,
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n_filters=n_filters, n_neurons_connected=n_neurons_connected,
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n_categories=n_categories, epochs=epochs, batch_size=batch_size,
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eta=eta, lmbd=lmbd)
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CNN.fit()
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print("Learning rate = ", eta)
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print("Lambda = ", lmbd)
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print("Test accuracy: %.3f" % CNN.test_accuracy)
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print()
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CNN_tf[i][j] = CNN
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# visual representation of grid search
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# uses seaborn heatmap, could probably do this in matplotlib
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import seaborn as sns
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sns.set()
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train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
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test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
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for i in range(len(eta_vals)):
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for j in range(len(lmbd_vals)):
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CNN = CNN_tf[i][j]
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train_accuracy[i][j] = CNN.train_accuracy
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test_accuracy[i][j] = CNN.test_accuracy
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fig, ax = plt.subplots(figsize = (10, 10))
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sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
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ax.set_title("Training Accuracy")
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ax.set_ylabel("$\eta$")
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ax.set_xlabel("$\lambda$")
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plt.show()
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fig, ax = plt.subplots(figsize = (10, 10))
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sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
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ax.set_title("Test Accuracy")
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ax.set_ylabel("$\eta$")
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ax.set_xlabel("$\lambda$")
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plt.show()
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!ec
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!split
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===== Running with Keras =====
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!bc pycod
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from keras.models import Sequential
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from keras.layers.convolutional import Conv2D
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from keras.layers.convolutional import MaxPooling2D
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from keras.layers import Flatten
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from keras.layers import Dense
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from keras.regularizers import l2
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from keras.optimizers import SGD
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def create_convolutional_neural_network_keras(input_shape, receptive_field,
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n_filters, n_neurons_connected, n_categories,
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eta, lmbd):
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model = Sequential()
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model.add(Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same',
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activation='relu', kernel_regularizer=l2(lmbd)))
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model.add(MaxPooling2D(pool_size=(2, 2)))
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model.add(Flatten())
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model.add(Dense(n_neurons_connected, activation='relu', kernel_regularizer=l2(lmbd)))
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model.add(Dense(n_categories, activation='softmax', kernel_regularizer=l2(lmbd)))
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sgd = SGD(lr=eta)
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model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
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return model
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epochs = 100
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batch_size = 100
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input_shape = X_train.shape[1:4]
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receptive_field = 3
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n_filters = 10
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n_neurons_connected = 50
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n_categories = 10
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eta_vals = np.logspace(-5, 1, 7)
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lmbd_vals = np.logspace(-5, 1, 7)
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CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
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for i, eta in enumerate(eta_vals):
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for j, lmbd in enumerate(lmbd_vals):
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CNN = create_convolutional_neural_network_keras(input_shape, receptive_field,
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n_filters, n_neurons_connected, n_categories,
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eta, lmbd)
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CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
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scores = CNN.evaluate(X_test, Y_test)
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CNN_keras[i][j] = CNN
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print("Learning rate = ", eta)
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print("Lambda = ", lmbd)
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print("Test accuracy: %.3f" % scores[1])
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print()
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# visual representation of grid search
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# uses seaborn heatmap, could probably do this in matplotlib
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import seaborn as sns
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sns.set()
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train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
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test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
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for i in range(len(eta_vals)):
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for j in range(len(lmbd_vals)):
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CNN = CNN_keras[i][j]
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train_accuracy[i][j] = CNN.evaluate(X_train, Y_train)[1]
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test_accuracy[i][j] = CNN.evaluate(X_test, Y_test)[1]
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fig, ax = plt.subplots(figsize = (10, 10))
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sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
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ax.set_title("Training Accuracy")
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ax.set_ylabel("$\eta$")
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ax.set_xlabel("$\lambda$")
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plt.show()
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fig, ax = plt.subplots(figsize = (10, 10))
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sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
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ax.set_title("Test Accuracy")
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ax.set_ylabel("$\eta$")
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ax.set_xlabel("$\lambda$")
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plt.show()
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