机器学习（线性回归）

线性模型

损失函数

原理：给定原始x,y值，对权重w值从[0:4]中以0.1间隔随机取值，设置预测线性函数y=x*w,对预测值与原始y值进行loss计算，并画出预测图像

x	y	y_predit	loss
1	2	3	1
2	4	6	4
3	6	9	9
			mean=14/3

源代码

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]

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

# 损失函数
def loss(x, y):
    y_pred = forward(x)
    return (y_pred - y) * (y_pred - y)

#权重准备空列表
w_list = []
mse_list = []

for w in np.arange(0.0, 4.1, 0.1):
# Print the weights and initialize the lost
    print("w=", w)
    l_sum = 0
    for x_val, y_val in zip(x_data, y_data):

# For each input and output, calculate y_hat
# Compute the total loss and add to the total error
        y_pred_val = forward(x_val)#计算预测值
        l = loss(x_val, y_val)#计算损失
        l_sum += l
        print("\t", x_val, y_val, y_pred_val, l)
# Now compute the Mean squared error (mse) of each
# Aggregate the weight/mse from this run
    print("MSE=", l_sum / 3)#mse均方误差
    w_list.append(w)
    mse_list.append(l_sum / 3)

# Plot it all
plt.plot(w_list, mse_list)
plt.ylabel('Loss')
plt.xlabel('w')
plt.show()

结果

损失在w=2时为最小，为最优值

优化

当数据集过大时，可用visdom实时绘画

Exercise

问题

• Try to use the model in right-side, and draw the cost graph
• Tips

1. you can read the material of how to draw 3d graph
2. Function np.meshgrid() is poplular for drawing 3d graph,read the [docs] and utilize vectorization caluation.

线性模型

源代码

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

x = np.arange(-2.0, 2.0 , 0.01)
y = np.arange(-4.0, 4.0 , 0.01)
w = np.arange(-0.0, 4.0, 0.01)
b = np.arange(-2.0, 2.0, 0.01)
# our model for the forward pass
def forward(x):
    return x * w+b

# 损失函数
def loss(x, y):
    y_pred = forward(x)
    return (y_pred - y) * (y_pred - y)

figure = plt.figure()
ax = Axes3D(figure)
x,y=np.meshgrid(x,y)
z=loss(x,y)

ax.plot_surface(b,w,z,rstride=1,cstride=1,cmap='rainbow')

ax.set_xlabel('b')
ax.set_ylabel('w')
ax.set_zlabel('Loss')
plt.show()

结果

从图可以看出，当w=2，b=0时，误差最小。