Pytorch深度学习实践（二）—— 线性模型-优快云博客

该博客探讨了线性模型在预测中的应用，从简单的y=wx模型开始，通过计算均方误差（MSE）作为损失函数。随着模型扩展为y=wx-b，损失函数随之改变，导致结果展示从二维平面上升到三维空间。博主通过代码展示了如何绘制三维损失曲面，并解释了参数w和b如何影响模型的性能。

import numpy as np
import matplotlib.pyplot as plt

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

def forward(x):
    return x * w

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

w_list = []
mse_list = []
for w in np.arange(0.0, 4.1, 0.1):
    print('w=',w)
    l_sum = 0
    for x_val, y_val in zip(x_data, y_data):
        y_pred_val = forward(x_val)
        loss_val = loss(x_val, y_val)
        l_sum += loss_val
        print('\t', x_val, y_val, y_pred_val, loss_val)
    print('MSE=', l_sum/3)
    w_list.append(w)
    mse_list.append(l_sum/3)
plt.plot(w_list, mse_list)
plt.ylabel('MSE')
plt.xlabel('w')
plt.show()

结果如下：
MSE:平均平方误差该图目的是寻找使得Loss最小的w值
输出展示
课后作业：
将线性模型由 y(hat) = x * w 改为 y(hat) = x * w - b
损失函数发生改变，结果图由二维变为三维

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

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

def forward(x):
    return x * w - b

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

mse_list = []
W = np.arange(0.0,4.1,0.1)
B = np.arange(0.0,4.1,0.1)
[w,b]=np.meshgrid(W,B)      #生成坐标点的网格矩阵,自动进行二次循环

l_sum = 0
for x_val, y_val in zip(x_data, y_data):
    y_pred_val = forward(x_val)
    print(y_pred_val)
    loss_val = loss(x_val, y_val)
    l_sum += loss_val

fig = plt.figure()
ax = Axes3D(fig)
ax.plot_surface(w, b, l_sum/3)
plt.show()