优化算法——梯度下降法实现

版权声明：test https://blog.csdn.net/weixin_37275456/article/details/83302091

批量梯度下降算法实现

import numpy as np

# 设置数据集的行数和维数
r = 20
c = 10

# 生成数据集合label

x = np.random.randint(0, 10, r * c).reshape(r, c)  # 20行，10列
x = np.hstack((x, np.ones(r).reshape(r, 1)))  # 20行，11列

y = np.random.randint(0, 1, r).reshape(r, 1)  # 20行，1列


# 代价函数
def cost(x, y, theta, m):
    diff = np.dot(x, theta) - y
    return (1 / (2 * m)) * np.dot(np.transpose(diff), diff)


# 梯度函数
def grad(x, y, theta, m):
    diff = np.dot(x, theta) - y
    return 1 / m * np.dot(np.transpose(x), diff)  # 结果是一列


def gradient_descent(x, y, num, error):
    m = x.shape[0]  # 20行
    theta = np.random.randint(0, 10, c + 1).reshape(c + 1, 1)  # 20行一列
    time = 0
    while cost(x, y, theta, m) > error and time < num:
        theta = theta - 0.001 * grad(x, y, theta, m)
        time += 1

    print(cost(x, y, theta, m))
    return theta


ans = gradient_descent(x, y, 10000, 0.01)
print(ans)

随机梯度下降算法实现

import numpy as np
import time

# 设置数据集的行数和维数
r = 20
c = 10

# 生成数据集合label
x = np.random.randint(0, 100, r * c).reshape(r, c)  # 20行，10列
x = np.hstack((x, np.ones(r).reshape(r, 1)))  # 20行，11列
# print(x)
y = np.random.randint(0, 100, r).reshape(r, 1)  # 20行，1列
# print(y)


# 损失函数
def cost(x, y, theta, m):
    diff = np.dot(x, theta) - y
    return (1 / (2 * m)) * np.dot(np.transpose(diff), diff)


# 梯度函数，给样本（xi,yi)求第j个theta的偏导数
def grad(xi, yi, theta, j, m):  # 明确选定的theta的第几个值
    return 1. / m *(np.dot(xi, theta) - yi) * xi[j]


def gradient_descent(x, y, num, error):
    m = x.shape[0]  # 20行
    theta = np.random.random(c + 1).reshape(c + 1, 1)  # 这里不能用随机整数，无法更新
    time = 0
    while cost(x, y, theta, m) > error and time < num:
        index = np.random.randint(m)
        xi = x[index]
        yi = y[index]
        for i in range(11):  # 依次更新theta
            gr = grad(xi, yi, theta, i , 20)
            theta[i] = theta[i] - 0.0001*gr
        time += 1

    print(cost(x, y, theta, m))
    return theta

ans = gradient_descent(x, y, 1000, 0.01)

print(np.dot(x, ans) - y)
print(ans)