PythonDNNPractice.py

# # #
# Tutorial from: 
# http://www.wildml.com/2015/09/implementing-a-neural-network-from-scratch/
# This uses CPU only so be aware of your computer specifications
# # #

import sklearn
from sklearn import *
import numpy as np
import matplotlib.pyplot as plt

np.random.seed(0)

# # #
# Generate a dataset and plot it
# # #

# Below is the original dataset from tutorial
# X, y = sklearn.datasets.make_moons(200, noise=0.20)

# Custom dataset
# This dataset has 2 classes:
# [0]: y = x
# [1]: y = x^2

# WARNING: more than 20 datas can end up PC freezing
X = []
for i in range(5):
    X.append([i, i, 0])
    X.append([i, i**2, 1])

X = np.array(X)
y = X[:, 2]
X = X[:, [0,1]]

# Plot
plt.scatter(X[:,0], X[:,1], s=None, c=y, cmap=plt.cm.Spectral)

# # #
# Use Logistic Regression method
# # #

# Train the logistic rgeression classifier
clf = sklearn.linear_model.LogisticRegressionCV()

# Fit the data
clf.fit(X, y)
 
# Helper function to plot a decision boundary.
# If you don't fully understand this function don't worry, it just generates the contour plot below.
def plot_decision_boundary(pred_func):
    # Set min and max values and give it some padding
    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
    h = 0.01
    # Generate a grid of points with distance h between them
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    # Predict the function value for the whole gid
    Z = pred_func(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)
    # Plot the contour and training examples
    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
    plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)

# Plot the decision boundary
plot_decision_boundary(lambda x: clf.predict(x))
plt.title("Logistic Regression")
plt.show()

# # #
# Build a custom Deep Neural Network:
# Model: Input(2) -> HiddenLayer1(5) -> Output(2)
# # #

num_examples = len(X) # training set size
nn_input_dim = 2 # input layer dimensionality
nn_output_dim = 3 # output layer dimensionality
 
# Gradient descent parameters (I picked these by hand)
epsilon = 0.01 # learning rate for gradient descent
reg_lambda = 0.01 # regularization strength

# Helper function to evaluate the total loss on the dataset
def calculate_loss(model):
    W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
    # Forward propagation to calculate our predictions
    # input of hidden layer 1
    z1 = X.dot(W1) + b1
    # output of hidden layer 1 by tanh activation
    a1 = np.tanh(z1)
    # input of output layer 2
    z2 = a1.dot(W2) + b2
    # output of output layer 2 by softmax activation
    exp_scores = np.exp(z2)
    probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
    # Calculating the loss
    corect_logprobs = -np.log(probs[range(num_examples), y])
    data_loss = np.sum(corect_logprobs)
    # Add regulatization term to loss (optional)
    data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))
    return 1./num_examples * data_loss

# Helper function to predict an output (0 or 1)
def predict(model, x):
    W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']
    # Forward propagation
    z1 = x.dot(W1) + b1
    a1 = np.tanh(z1)
    z2 = a1.dot(W2) + b2
    exp_scores = np.exp(z2)
    probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
    return np.argmax(probs, axis=1)

# This function learns parameters for the neural network and returns the model.
# - nn_hdim: Number of nodes in the hidden layer
# - num_passes: Number of passes through the training data for gradient descent
# - print_loss: If True, print the loss every 1000 iterations
def build_model(nn_hdim, num_passes=20000, print_loss=False):
     
    # Initialize the parameters to random values. We need to learn these.
    np.random.seed(0)
    W1 = np.random.randn(nn_input_dim, nn_hdim) / np.sqrt(nn_input_dim)
    b1 = np.zeros((1, nn_hdim))
    W2 = np.random.randn(nn_hdim, nn_output_dim) / np.sqrt(nn_hdim)
    b2 = np.zeros((1, nn_output_dim))
 
    # This is what we return at the end
    model = {}
     
    # Gradient descent. For each batch...
    for i in xrange(0, num_passes):
 
        # Forward propagation
        z1 = X.dot(W1) + b1
        a1 = np.tanh(z1)
        z2 = a1.dot(W2) + b2
        exp_scores = np.exp(z2)
        probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
 
        # Backpropagation
        delta3 = probs
        delta3[range(num_examples), y] -= 1
        dW2 = (a1.T).dot(delta3)
        db2 = np.sum(delta3, axis=0, keepdims=True)
        delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))
        dW1 = np.dot(X.T, delta2)
        db1 = np.sum(delta2, axis=0)
 
        # Add regularization terms (b1 and b2 don't have regularization terms)
        dW2 += reg_lambda * W2
        dW1 += reg_lambda * W1
 
        # Gradient descent parameter update
        W1 += -epsilon * dW1
        b1 += -epsilon * db1
        W2 += -epsilon * dW2
        b2 += -epsilon * db2
         
        # Assign new parameters to the model
        model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}
         
        # Optionally print the loss.
        # This is expensive because it uses the whole dataset, so we don't want to do it too often.
        if print_loss and i % 1000 == 0:
          print "Loss after iteration %i: %f" %(i, calculate_loss(model))
     
    return model

# Build a model with a 3-dimensional hidden layer
# WARNING: 3 is enough for CPU, more than 3 can end up PC freezing
model = build_model(3, print_loss=True)
 
# Plot the decision boundary
plot_decision_boundary(lambda x: predict(model, x))
plt.title("Decision Boundary for hidden layer size 3")
plt.show()