【Pytorch基础】torch.nn.MSELoss损失函数
MSE: Mean Squared Error(均方误差)
含义:均方误差,是预测值与真实值之差的平方和的平均值,即:
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\begin{aligned} MSE =\cfrac {1}{N}\sum_{i=1}^n(x_i-y_i)^2 \end{aligned}
MSE=N1i=1∑n(xi−yi)2
但是,在具体的应用中跟定义稍有不同。主要差别是参数的设置,在torch.nn.MSELoss中有一个reduction参数。reduction是维度要不要缩减以及如何缩减主要有三个选项:
- ‘none’:no reduction will be applied.
- ‘mean’: the sum of the output will be divided by the number of elements in the output.
- ‘sum’: the output will be summed.
如果不设置reduction参数,默认是’mean’。
下面看个例子:
import torch
import torch.nn as nn
a = torch.tensor([[1, 2],
[3, 4]], dtype=torch.float)
b = torch.tensor([[3, 5],
[8, 6]], dtype=torch.float)
loss_fn1 = torch.nn.MSELoss(reduction='none')
loss1 = loss_fn1(a.float(), b.float())
print(loss1) # 输出结果:tensor([[ 4., 9.],
# [25., 4.]])
loss_fn2 = torch.nn.MSELoss(reduction='sum')
loss2 = loss_fn2(a.float(), b.float())
print(loss2) # 输出结果:tensor(42.)
loss_fn3 = torch.nn.MSELoss(reduction='mean')
loss3 = loss_fn3(a.float(), b.float())
print(loss3) # 输出结果:tensor(10.5000)
在loss1中是按照原始维度输出,即对应位置的元素相减然后求平方;loss2中是对应位置求和;loss3中是对应位置求和后取平均。
除此之外,torch.nn.MSELoss还有一个妙用,求矩阵的F范数(F范数详解)当然对于所求出来的结果还需要开方。