Linear regression with gradient descent

linear_regression.py

# How to Do Linear Regression using Gradient Descent

# import Numpy, THE matrix multiplication library for python
from numpy import *

# minimize the "sum of squared errors". This is how we calculate and correct our error
def compute_error_for_line_given_points(b, m, points):
    totalError = 0
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        totalError += (y - (m * x + b)) **2
    return totalError / float(len(points))


def step_gradient(b_current, m_current, points, learning_rate):
    # gradient descent
    b_gradient = 0
    m_gradient = 0
    N = float(len(points))
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]

        # direction with respecto to b and m
        # computing partial derivatives of our error function
        b_gradient += -(2/N) * (y - ((m_current * x) + b_current))
        m_gradient += -(2/N) * x * (y - ((m_current * x) + b_current))
    new_b = b_current - (learning_rate * b_gradient)
    new_m = m_current - (learning_rate * m_gradient)
    return [new_m, new_m]

def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations):
    b = starting_b
    m = starting_m

    for i in range(num_iterations):
        b, m = step_gradient(b, m, array(points), learning_rate)
    return [b, m]

def run():
    # Step 1 - Collect our data
    points = genfromtxt("data.csv", delimiter=",")

    # Step 2 - Define our hyperparameters.
    # The learning rate defines how fast our model learns (converges).
    learning_rate = 0.0001
    # y = mx + b (slope formula)
    initial_b = 0
    initial_m = 0
    num_iterations = 1000 # it depends on the dimensions of the dataset

    # step 3 - train our model
    print("Starting gradient descent at b = {0}, m = {1}, error = {2}".format(initial_b, initial_m, compute_error_for_line_given_points(initial_b, initial_m, points)))
    print("Running...")
    [b, m] = gradient_descent_runner(points, initial_b, initial_m, learning_rate, num_iterations)
    print("After {0} iterations b = {1}, m = {2}, error = {3}".format(num_iterations, b, m, compute_error_for_line_given_points(b, m, points)))


if __name__ == '__main__':
    run()