标签：1.0 Linear 3.0 6.0 Model 2.0 MSE 4.0
Linear Model
机器学习
\(x\)为学习时间，\(y\)为学习该时间能够在考试中取得的分数
在这里来为这些数据寻求一个最好的模型
线性回归
Linear Model：\(\hat{y}=x*w\)
训练损失 (误差)
MSE（Mean Squared Mean）均方误差：
\[loss=(\hat{y}-y)^2=(x*w-y)^2 \]| \(x\ (Hours)\) | \(y \ (Points)\) | \(y\)_\(predict\ (w=3)\) | \(Loss\ (w=3)\) |
|---|---|---|---|
| 1 | 2 | 3 | 1 |
| 2 | 4 | 6 | 4 |
| 3 | 6 | 9 | 9 |
| \(mean=14/3\) |
| \(x\ (Hours)\) | \(y \ (Points)\) | \(y\)_\(predict\ (w=3)\) | \(Loss\ (w=3)\) |
|---|---|---|---|
| 1 | 2 | 4 | 4 |
| 2 | 4 | 8 | 16 |
| 3 | 6 | 12 | 36 |
| \(mean=56/3\) |
| \(x\ (Hours)\) | \(Loss\ (w=0)\) | \(Loss\ (w=1)\) | \(Loss\ (w=2)\) | \(Loss\ (w=3)\) | \(Loss\ (w=4)\) |
|---|---|---|---|---|---|
| 1 | 4 | 1 | 0 | 1 | 4 |
| 2 | 16 | 4 | 0 | 4 | 16 |
| 3 | 36 | 9 | 0 | 9 | 36 |
| \(MSE\) | 18.7 | 4.7 | 0 | 4.7 | 18.7 |
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 # 定义线性模型：y=x*w
def loss(x, y):
y_pred = forward(x)
return (y_pred-y)**2 # 定义损失函数(y_pred-y)^2
w_list = []
mse_list = []
for w in np.arange(0.0, 4.1, 0.1): # w从0.0取到4.1间隔0.1
print('w=', w)
l_sum = 0 # 重置总损失为0
for x_val, y_val in zip(x_data, y_data): # 成对提取x,y
y_pred_val = forward(x_val) # 获得y_pred
loss_val = loss(x_val, y_val) # 计算损失函数Loss
l_sum += loss_val # 将损失添加到总损失中
print('\t', x_val, y_val, y_pred_val, loss_val)
print('MSE',l_sum/3) # 计算均方误差
w_list.append(w) # 将w添加到列表中
mse_list.append(l_sum/3) # 将均方误差添加到列表中
w= 1.9000000000000001
1.0 2.0 1.9000000000000001 0.009999999999999974
2.0 4.0 3.8000000000000003 0.0399999999999999
3.0 6.0 5.7 0.0899999999999999
MSE 0.046666666666666586
w= 2.0
1.0 2.0 2.0 0.0
2.0 4.0 4.0 0.0
3.0 6.0 6.0 0.0
MSE 0.0
w= 2.1
1.0 2.0 2.1 0.010000000000000018
2.0 4.0 4.2 0.04000000000000007
3.0 6.0 6.300000000000001 0.09000000000000043
MSE 0.046666666666666835
w= 2.2
1.0 2.0 2.2 0.04000000000000007
2.0 4.0 4.4 0.16000000000000028
3.0 6.0 6.6000000000000005 0.36000000000000065
MSE 0.18666666666666698
w= 2.3000000000000003
1.0 2.0 2.3000000000000003 0.09000000000000016
2.0 4.0 4.6000000000000005 0.36000000000000065
3.0 6.0 6.9 0.8100000000000006
MSE 0.42000000000000054
w= 2.4000000000000004
1.0 2.0 2.4000000000000004 0.16000000000000028
2.0 4.0 4.800000000000001 0.6400000000000011
3.0 6.0 7.200000000000001 1.4400000000000026
MSE 0.7466666666666679
w= 2.5
1.0 2.0 2.5 0.25
2.0 4.0 5.0 1.0
3.0 6.0 7.5 2.25
MSE 1.1666666666666667
w= 2.6
1.0 2.0 2.6 0.3600000000000001
2.0 4.0 5.2 1.4400000000000004
3.0 6.0 7.800000000000001 3.2400000000000024
MSE 1.6800000000000008
w= 2.7
1.0 2.0 2.7 0.49000000000000027
2.0 4.0 5.4 1.960000000000001
3.0 6.0 8.100000000000001 4.410000000000006
MSE 2.2866666666666693
w= 2.8000000000000003
1.0 2.0 2.8000000000000003 0.6400000000000005
2.0 4.0 5.6000000000000005 2.560000000000002
3.0 6.0 8.4 5.760000000000002
MSE 2.986666666666668
w= 2.9000000000000004
1.0 2.0 2.9000000000000004 0.8100000000000006
2.0 4.0 5.800000000000001 3.2400000000000024
3.0 6.0 8.700000000000001 7.290000000000005
MSE 3.780000000000003
w= 3.0
1.0 2.0 3.0 1.0
2.0 4.0 6.0 4.0
3.0 6.0 9.0 9.0
MSE 4.666666666666667
w= 3.1
1.0 2.0 3.1 1.2100000000000002
2.0 4.0 6.2 4.840000000000001
3.0 6.0 9.3 10.890000000000004
MSE 5.646666666666668
w= 3.2
1.0 2.0 3.2 1.4400000000000004
2.0 4.0 6.4 5.760000000000002
3.0 6.0 9.600000000000001 12.96000000000001
MSE 6.720000000000003
w= 3.3000000000000003
1.0 2.0 3.3000000000000003 1.6900000000000006
2.0 4.0 6.6000000000000005 6.7600000000000025
3.0 6.0 9.9 15.210000000000003
MSE 7.886666666666668
w= 3.4000000000000004
1.0 2.0 3.4000000000000004 1.960000000000001
2.0 4.0 6.800000000000001 7.840000000000004
3.0 6.0 10.200000000000001 17.640000000000008
MSE 9.14666666666667
w= 3.5
1.0 2.0 3.5 2.25
2.0 4.0 7.0 9.0
3.0 6.0 10.5 20.25
MSE 10.5
plt.plot(w_list,mse_list)
plt.ylabel('Loss')
plt.xlabel('w')
plt.show()
标签：1.0,Linear,3.0,6.0,Model,2.0,MSE,4.0 来源： https://www.cnblogs.com/Reion/p/15381272.html
本站声明： 1. iCode9 技术分享网（下文简称本站）提供的所有内容，仅供技术学习、探讨和分享； 2. 关于本站的所有留言、评论、转载及引用，纯属内容发起人的个人观点，与本站观点和立场无关； 3. 关于本站的所有言论和文字，纯属内容发起人的个人观点，与本站观点和立场无关； 4. 本站文章均是网友提供，不完全保证技术分享内容的完整性、准确性、时效性、风险性和版权归属；如您发现该文章侵犯了您的权益，可联系我们第一时间进行删除； 5. 本站为非盈利性的个人网站，所有内容不会用来进行牟利，也不会利用任何形式的广告来间接获益，纯粹是为了广大技术爱好者提供技术内容和技术思想的分享性交流网站。