mlp_scratch.py

import numpy as np 
from sklearn import datasets,linear_model
import matplotlib.pyplot as plt

# Generate a dataset and plot it
np.random.seed(0)
X,y = datasets.make_moons(200, noise=0.20)
plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral)
plt.show()

# Train the logistic regression classifier
clf=linear_model.LogisticRegressionCV()
clf.fit(X,y)

# Helper function to plot a decision boundary
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 value for the whole grid
	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()

num_examples=len(X) # training set size
nn_input_dim=2 # input layer dimensionality
nn_output_dim=2 # output layer dimensionality

# Gradient descent parameters 
epsilon=0.01 # learning rate for gradient descent
reg_lambda=0.01 #regularization length

# 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
	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)
	# Calculating the loss
	corect_logprobs=-np.log(probs[range(num_examples),y])
	data_loss=np.sum(corect_logprobs)
	# Add regularization 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 100 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 range(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)
		# Back propagation
		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, ": ", calculate_loss(model))
	return model

# Build a model with a 3-dimensional hidden layer
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()

# Varying the hidden layer size
plt.figure(figsize=(16, 32))
hidden_layer_dimensions = [1, 2, 3, 4, 5, 20, 50]
for i, nn_hdim in enumerate(hidden_layer_dimensions):
	plt.subplot(4, 2, i+1)
	plt.title('Hidden Layer size %d' % nn_hdim)
	model = build_model(nn_hdim)
	plot_decision_boundary(lambda x: predict(model, x))

plt.show()