代码示例来自 Udacity 课程中 Siraj 的一个教学视频，版权归属于原作者及 Udacity 所有，源代码及数据源可见 Siraj 的 Github，尽管代码可以直接下载，我还是选择跟随视频手动完成的方式，也对于引用方式和变量命名做了一点修改，放在这里方便随时查看。
这个代码示例主要是为了演示梯度下降的实现过程，用它来求解线性回归稍微有些大材小用，但不妨碍说明问题。
import numpy as np
def compute_error_for_points(b, m, points):
total_error = 0
for i in range(len(points)):
x = points[i, 0]
y = points[i, 1]
total_error += (y - (m * x + b)) ** 2
return total_error / float(len(points))
def step_gradient(b_current, m_current, points, learning_rate):
# core gradient descent computation
b_gradient = 0
m_gradient = 0
N = float(len(points))
for i in range(len(points)):
x = points[i, 0]
y = points[i, 1]
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_b, 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, np.array(points), learning_rate)
return [b, m]
def run():
points = np.genfromtxt('data.csv', delimiter=',')
# hyperparameters
learning_rate = 0.0001
# y = mx + b
initial_b = 0
initial_m = 0
num_iterations = 1000
[b, m] = gradient_descent_runner(points, initial_b, initial_m, learning_rate, num_iterations)
print(b)
print(m)
if __name__ == '__main__':
run()
