For this lab, you will be tasked with building a neural network that takes in an

Question

For this lab, you will be tasked with building a neural network that takes in an a text file with a set of data and then trains the network on that said data. In addition to that, you will need to provide the user with command line interface which will prompt the user for an input and then provide an output.

Every node will need to have to use a nonlinear function which will work as it’s activation function a good example would be a sigmoid function.

Your network will need to have a condition which will make it stop. Preferably you want it to be so that you would stop when your error levels are bellow a specific desired value.

You can test this code by training the network to recolonize a logic gate.

Explanation / Answer

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

class Config:
nn_input_dim = 2 # input layer dimensionality
nn_output_dim = 2 # 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

def generate_data():
np.random.seed(0)
X, y = datasets.make_moons(200, noise=0.20)
return X, y

def visualize(X, y, model):
# plt.scatter(X[:, 0], X[:, 1], s=40, c=y, cmap=plt.cm.Spectral)
# plt.show()
plot_decision_boundary(lambda x:predict(model,x), X, y)
plt.title("Logistic Regression")

def plot_decision_boundary(pred_func, X, y):
# 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)
plt.show()

# Helper function to evaluate the total loss on the dataset
def calculate_loss(model, X, y):
num_examples = len(X) # training set size
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 regulatization term to loss (optional)
data_loss += Config.reg_lambda / 2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))
return 1. / num_examples * data_loss

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(X, y, nn_hdim, num_passes=20000, print_loss=False):
# Initialize the parameters to random values. We need to learn these.
num_examples = len(X)
np.random.seed(0)
W1 = np.random.randn(Config.nn_input_dim, nn_hdim) / np.sqrt(Config.nn_input_dim)
b1 = np.zeros((1, nn_hdim))
W2 = np.random.randn(nn_hdim, Config.nn_output_dim) / np.sqrt(nn_hdim)
b2 = np.zeros((1, Config.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)

# 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 += Config.reg_lambda * W2
dW1 += Config.reg_lambda * W1

# Gradient descent parameter update
W1 += -Config.epsilon * dW1
b1 += -Config.epsilon * db1
W2 += -Config.epsilon * dW2
b2 += -Config.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, X, y)))

return model

def main():
X, y = generate_data()
model = build_model(X, y, 3, print_loss=True)
visualize(X, y, model)

if __name__ == "__main__":
main()

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