Simple Regression Implenmentation

最新推荐文章于 2025-12-05 17:02:52 发布

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本文介绍了一种使用梯度下降法来寻找最佳线性回归模型的方法。通过给定的数据点，逐步调整权重和偏置，以最小化损失函数（均方误差）。演示了从初始化参数到实现梯度下降的完整过程。

Give the points as below:

x	y
1	3
2	5
3	7
4	9

try to find the optiaml function y = w * x + b to fit the points above.

The code as below:

import numpy as np


def compute_mse(w, b, points):
    total_error = 0
    for i in range(len(points)):
        x = points[i][0]
        y = points[i][1]
        total_error += ((w * x + b) - y) ** 2
    return total_error / float(len(points))


def compute_step_grad(curr_w, curr_b, points, lr):
    grad_w = 0
    grad_b = 0
    N = float(len(points))
    for i in range(len(points)):
        x = points[i][0]
        y = points[i][1]
        grad_w += 2 * (curr_w * x + curr_b - y) * x / N
        grad_b += 2 * (curr_w * x + curr_b - y) / N
    next_w = curr_w - lr * grad_w
    next_b = curr_b - lr * grad_b
    return [next_w, next_b]


def gradient_descent(init_w, init_b, points, lr, iters):
    curr_w, curr_b = init_w, init_b
    for i in range(iters):
        curr_w, curr_b = compute_step_grad(curr_w, curr_b, points, lr)
    return [curr_w, curr_b]


def main():
    points = np.genfromtxt('points.csv',delimiter=',')
    init_w = 0.5
    init_b = 0.1
    lr = 0.01
    iters = 1000
    curr_w, curr_b = gradient_descent(init_w, init_b, points, lr, iters)
    print('--------------------------------------')
    print('initial w = {}, b = {}, mse = {}.'.format(init_w, init_b, compute_mse(init_w, init_b, points)))
    print('--------------------------------------')
    print('after gradient descent, current w = {}, b = {}, mese = {}.'.format(curr_w, curr_b, compute_mse(curr_w, curr_b, points)))


if __name__ == "__main__":
    main()