Deep Learning_Loss Functions

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A loss function is a function L:(z,y)∈R×YL(z,y)∈R that takes as inputs the predicted value z corresponding to the real data value y and outputs how different they are.

The common loss functions are summed up in the table below:

Least squared error

Logistic loss

Hinge loss

Cross-entropy

1/2(yz)2

log(1+exp(−yz))

max(0,1−yz)

−[ylog(z)+(1−y)log(1−z)]

Linear regression

Logistic regression

SVM

Neural Network