0_gradient_descent.py

import numpy as np


def compute_error_for_line_given_points(b, w, points):
    # 初始化误差
    total_error = 0
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        # 计算误差平方和
        total_error += (y - (w * x + b)) ** 2

    # 每个数据的平均误差
    return total_error / float(len(points))


def step_gradient(b_current, w_current, points, learning_rate):
    b_gradient = 0
    w_gradient = 0
    n = float(len(points))
    for i in range(0, len(points)):
        x = points[i, 0]
        y = points[i, 1]
        # 更新梯度
        b_gradient += (2/n) * ((w_current * x + b_current) - y)
        w_gradient += (2/n) * x * ((w_current * x + b_current) - y)

    new_b = b_current - (learning_rate * b_gradient)
    new_w = w_current - (learning_rate * w_gradient)
    return [new_b, new_w]


def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):
    b = starting_b
    w = starting_w
    for i in range(num_iterations):
        b, w = step_gradient(b, w, np.array(points), learning_rate)
    return [b, w]


def run():
    points = np.genfromtxt("data/data.csv", delimiter=",")
    learning_rate = 0.0001
    initial_b = 0  # initial y-intercept guess
    initial_w = 0  # initial slope guess
    num_iterations = 1000
    print("Starting gradient descent at b = {0}, w = {1}, error = {2}"
          .format(initial_b, initial_w,
                  compute_error_for_line_given_points(initial_b, initial_w, points))
          )
    print("Running...")
    [b, w] = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)
    print("After {0} iterations b = {1}, w = {2}, error = {3}".
          format(num_iterations, b, w,
                 compute_error_for_line_given_points(b, w, points))
          )


if __name__ == '__main__':
    run()