mnist.py

import numpy as np
import pandas as pd
from matplotlib import pyplot as plt

# Import the data
data = pd.read_csv('/Users/catarina_palmeirao/Desktop/code/mnist/mnist_train.csv')

data = np.array(data)
m, n = data.shape
np.random.shuffle(data)

# Transpose and split the data
data_dev = data[0:1000].T
Y_dev = data_dev[0]
X_dev = data_dev[1:n]
X_dev = X_dev / 255.

data_train = data[1000:m].T
Y_train = data_train[0]
X_train = data_train[1:n]
X_train = X_train / 255.

# Initialize parameters with He initialization
def init_params():
    W1 = np.random.randn(10, 784) * np.sqrt(2. / 784)
    b1 = np.zeros((10, 1))
    W2 = np.random.randn(10, 10) * np.sqrt(2. / 10)
    b2 = np.zeros((10, 1))
    return W1, b1, W2, b2

# ReLU activation function
def ReLU(Z):
    return np.maximum(Z, 0)

# Softmax function
def softmax(Z):
    expZ = np.exp(Z - np.max(Z, axis=0, keepdims=True))
    return expZ / expZ.sum(axis=0, keepdims=True)

# Forward propagation
def forward_prop(W1, b1, W2, b2, X):
    Z1 = W1.dot(X) + b1
    A1 = ReLU(Z1)
    Z2 = W2.dot(A1) + b2
    A2 = softmax(Z2)
    return Z1, A1, Z2, A2

# One-hot encoding function
def one_hot(Y):
    one_hot_Y = np.zeros((Y.size, Y.max() + 1))
    one_hot_Y[np.arange(Y.size), Y] = 1
    return one_hot_Y.T

# Derivative of ReLU
def deriv_ReLU(Z):
    return Z > 0

# Backward propagation
def back_prop(Z1, A1, Z2, A2, W2, X, Y):
    m = Y.size
    one_hot_Y = one_hot(Y)
    dZ2 = A2 - one_hot_Y
    dW2 = 1 / m * dZ2.dot(A1.T)
    db2 = 1 / m * np.sum(dZ2, axis=1, keepdims=True)
    dZ1 = W2.T.dot(dZ2) * deriv_ReLU(Z1)
    dW1 = 1 / m * dZ1.dot(X.T)
    db1 = 1 / m * np.sum(dZ1, axis=1, keepdims=True)
    return dW1, db1, dW2, db2

# Update parameters
def update_params(W1, b1, W2, b2, dW1, db1, dW2, db2, alpha):
    W1 -= alpha * dW1
    b1 -= alpha * db1
    W2 -= alpha * dW2
    b2 -= alpha * db2
    return W1, b1, W2, b2

# Prediction function
def get_predictions(A2):
    return np.argmax(A2, axis=0)

# Accuracy calculation
def get_accuracy(predictions, Y):
    return np.sum(predictions == Y) / Y.size

# Compute cross-entropy loss
def compute_loss(A2, Y):
    m = Y.size
    one_hot_Y = one_hot(Y)
    log_probs = np.multiply(one_hot_Y, np.log(A2))
    loss = - np.sum(log_probs) / m
    return loss

# Gradient descent function with loss and accuracy monitoring
def gradient_descent(X, Y, alpha, iterations):
    W1, b1, W2, b2 = init_params()
    for i in range(iterations):
        Z1, A1, Z2, A2 = forward_prop(W1, b1, W2, b2, X)
        dW1, db1, dW2, db2 = back_prop(Z1, A1, Z2, A2, W2, X, Y)
        W1, b1, W2, b2 = update_params(W1, b1, W2, b2, dW1, db1, dW2, db2, alpha)
        
        if i % 50 == 0:
            loss = compute_loss(A2, Y)
            predictions = get_predictions(A2)
            accuracy = get_accuracy(predictions, Y)
            print(f"Iteration {i}: Loss = {loss:.4f}, Accuracy = {accuracy:.2f}")
            
    return W1, b1, W2, b2

# Train the model
W1, b1, W2, b2 = gradient_descent(X_train, Y_train, 0.1, 200)

# Evaluate on the development set
Z1_dev, A1_dev, Z2_dev, A2_dev = forward_prop(W1, b1, W2, b2, X_dev)
predictions_dev = get_predictions(A2_dev)
accuracy_dev = get_accuracy(predictions_dev, Y_dev)
print(f"Development Set Accuracy: {accuracy_dev:.2f}")


def make_predictions(X, W1, b1, W2, b2):
    _, _, _, A2 = forward_prop(W1, b1, W2, b2, X)
    predictions = get_predictions(A2)
    return predictions

def test_prediction(index, W1, b1, W2, b2):
    current_image = X_train[:, index, None]
    prediction = make_predictions(X_train[:, index, None], W1, b1, W2, b2)
    label = Y_train[index]
    print("Prediction: ", prediction)
    print("Label: ", label)
    
    current_image = current_image.reshape((28, 28)) * 255
    plt.gray()
    plt.imshow(current_image, interpolation='nearest')
    plt.show()

test_prediction(0, W1, b1, W2, b2)
test_prediction(1, W1, b1, W2, b2)
test_prediction(2, W1, b1, W2, b2)
test_prediction(3, W1, b1, W2, b2)

dev_predictions = make_predictions(X_dev, W1, b1, W2, b2)
get_accuracy(dev_predictions, Y_dev)