回歸問題常用的損失函數總結

1. 均方誤差MSE

歸一化的均方誤差（NMSE）

 

 

 2. 平均絕對誤差MAE

# true: 真目標變量的數組
# pred: 預測值的數組

def mse(true, pred): 
    return np.sum((true - pred)**2)
 
 def mae(true, pred):
  return np.sum(np.abs(true - pred))
 
 # 調用sklearn 
 from sklearn.metrics import mean_squared_error
 from sklearn.metrics import mean_absolute_error

3. Huber損失函數

 4. Log-Cosh損失函數

 

# huber 損失
def huber(true, pred, delta):
    loss = np.where(np.abs(true-pred) < delta , 0.5*((true-pred)**2), delta*np.abs(true - pred) - 0.5*(delta**2))
    return np.sum(loss)

# log cosh 損失
def logcosh(true, pred):
    loss = np.log(np.cosh(pred - true))
return np.sum(loss)

5. 實例

import numpy as np
import math

true = [0,1,2,3,4]
pred = [0,0,1,5,-11]

# MSE
mse = mean_squared_error(true,pred)
print("RMSE: ",math.sqrt(mse))

loss =0 
for i,j in zip(true,pred):
    loss += mse(i,j)
mseloss = math.sqrt(loss / len(true))
print("RMSE: ",mseloss)

#MAE
mae = mean_absolute_error(true,pred)
print("MAE: ",mae)

loss = 0
for i,j in zip(true,pred):
    loss += mae(i,j)
maeloss = loss / len(true)
print("MAE: ",maeloss)

#Huber
loss = 0
for i,j in zip(true,pred):
    loss += huber(i,j,1)
loss = loss / len(true)
print("Huber: ",loss)

#Log-Cosh
loss = 0
for i,j in zip(true,pred):
    loss += logcosh(i,j)
loss = loss / len(true)
print("Log-Cosh: ",loss)

6. tanh

Python中直接調用np.tanh() 即可計算。 

 

參考：https://zhuanlan.zhihu.com/p/39239829