一、Linear Model

1、Mde和lLoss函数的构建

2、计算权重w的损失loss

3、画出w和mse的关系图

4、全部整体的代码

import matplotlib.pyplot as plt
import numpy as np

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

# our model forward
def forward(x):
    return x*w

# Loss function

def loss(x, y):
    y_pred = forward(x)
    return (y_pred-y)*(y_pred-y)

# compute loss for w
w_list = []
mse_list = []
for w in np.arange(0.0, 4.1, 0.1):
    loss_sum = 0
    print("w = ", w)
    for x_val, y_val in zip(x_data, y_data):
        y_pred = forward(x_val)
        l = loss(x_val, y_val)
        loss_sum += l
        print("\t", x_val, y_val, y_pred, l)
    print("MSE = ", loss_sum/3)
    w_list.append(w)
    mse_list.append(loss_sum/3)

plt.plot(w_list, mse_list)
plt.xlabel("w")
plt.ylabel("loss")
plt.show()

二、Gradient Desent

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

w = 1.0  # any random value

# our model forward
def forward(x):
    return x*w

# Loss function

def loss(x, y):
    y_pred = forward(x)
    return (y_pred-y)*(y_pred-y)

# compute gradient
def gradient(x, y):
    return 2*x*(x*w - y)

# before training
print("predict (before training )", 4, forward(4))

# traning loop
for epoch in range(10):
    for x, y in zip(x_data, y_data):
        grad = gradient(x, y)
        w = w - 0.01 * grad
        print("\tgrad: ", x, y, grad)
        l = loss(x, y)
    print("", epoch, l)

# After traning
print("predict (After training )", 4, forward(4))

运行结果：

三、Back propogation

import torch
from torch.autograd import Variable

x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

w = Variable(torch.Tensor([1.0]), requires_grad=True)

# our model forward
def forward(x):
    return x*w

# Loss function
def loss(x, y):
    y_pred = forward(x)
    return (y_pred-y)*(y_pred-y)

# traning loop
for epoch in range(10):
    for x,y in zip(x_data, y_data):
        l = loss(x, y)
        l.backward()
        print("\tgrad:", x, y, w.grad.data[0])
        w.data = w.data - 0.01 * w.grad.data

        # manually zero the gradients after running the backward pass and update w
        w.grad.data.zero_()

    print("progress:", epoch, l.data[0])