机器学习-梯度下降算法案例

import numpy as np
"""
模拟数据集
"""
data = []
w = 1.477
b = 0.089
for i in range(100):
    x = np.random.uniform(-10.,10.)
    eps = np.random.normal(0.,0.1)
    y = 1.477*x + 0.089 + eps
    data.append([x,y])
"""
求均方差
"""
def mse(w,b,data):
    loss = 0
    for i in range(0,len(data)):
        x = data[i][0]
        y = data[i][1]
        loss += (y-w*x-b)**2
    return loss/float(len(data))
"""
计算梯度
lr:学习率
"""
def step_gradient(w,b,data,lr):
    b_gradient = 0
    w_gradient = 0
    m = float(len(data))
    for i in range(0,len(data)):
        x = data[i][0]
        y = data[i][1]
        b_gradient += (2/m) * (w*x+b-y)
        w_gradient += (2/m) * x * (w*x+b-y)
    new_w = w - lr*w_gradient
    new_b = b - lr*b_gradient
    return new_w,new_b
"""
梯度更新
lr:学习率
num:迭代次数
"""
def gradient_descent(data,start_b,start_w,lr,num):
    b = start_b
    w = start_w
    for step in range(num):
        w,b = step_gradient(w,b,np.array(data),lr)
        loss = mse(w,b,data)
        if step %50 == 0:
            print(step,w,b)
    return b,w
"""
梯度下降执行函数
"""
def main():
    lr = 0.001
    init_b = 0
    init_w = 0
    num = 1000
    b,w = gradient_descent(data,init_b,init_w,lr,num)
    lose = mse(w,b,data)
    print("
")
    print(lose,w,b)  # 0.008130636177163393 1.4743398873266684 0.08602558343646888
main()

 Pytorch

import torch
import numpy as np
import matplotlib
"""
1准备数据
2通过模型计算predict
3计算loss
4方向传播，更新参数
"""
#y = 3*x+1.2
x = torch.rand([500,1])
y = x*3+1.2
w = torch.rand([1,1],requires_grad=True)
b = torch.tensor(0,requires_grad=True,dtype=torch.float32)


for i in range(500):
    y_predict = torch.matmul(x, w) + b
    loss = (y_predict - y).pow(2).mean()
    if w.grad is not None:
        w.grad.data.zero_()
    if b.grad is not None:
        b.grad.data.zero_()
    loss.backward()
    w.data = w.data - w.grad * 0.1
    b.data = b.data - b.grad * 0.1
    print(w,b,loss)