Simple Machine Learning Implementations

linear-regression.py

import random
import numpy as np

# Define Simple Dataset generated using the linear equation y = 4 * x0 + 9 * x1 + 13 with some noise added in
def generate_dataset(n_rows=100):
    # 1. Generate a raw NumPy array (n_rows by 2 columns)
    raw_data = np.random.rand(n_rows, 2)
    
    # 2. Perform the math using NumPy indexing (very fast)
    # y = 4 * x0 + 9 * x1 + 13
    y = 4 * raw_data[:, 0] + 9 * raw_data[:, 1] + 13 + (random.random() * random.choice([-1, 1]))
    
    return raw_data, y



# Generate a dataset
X, y = generate_dataset(1000)

learning_rate = 0.01
iterations = 10000

n_samples, n_features = X.shape

# We have n_features. To include the bias (theta_0) in the matric operation, we are adding a new feature X_0 (all 1s)
X_with_bias = np.c_[np.ones(n_samples), X]

theta = np.zeros((n_features+1, 1))

# Convert y to a column vector
y = y.reshape(-1, 1)


for _ in range(iterations):
    # h_theta(x) = X . theta (Matrix Multiplication)
    predictions = X_with_bias @ theta

    errors = predictions - y

    # Taking the average gradients because we don't want the gradients to scale with the size of the dataset
    gradient = (1/n_samples) * X_with_bias.T @ errors

    theta -= (learning_rate * gradient)

# Theta gets computed to the values below or something close (due to the random noise in the data)
# [[12.40251102]
#  [ 4.00076841]
#  [ 8.99951281]]
print(theta)