Does sigmoid function really matter in logistic regression?

Question

I implemented a binary logistic regression classifier. To play, I replaced the sigmoid function (1/1 + exp (-z)) with tanh. The results were exactly the same, with the same threshold of 0.5 for classification, and although tanh is in the range {-1.1}, while the sigmoid is in the range {0.1}.

Does it really matter that we use a sigmoid function, or can any differentiable nonlinear function, such as tanh, work?

Thanks.

Answer 1

, , tanh?

, , , . tanh:

sigmoid: http://www.wolframalpha.com/input/?i=plot+sigmoid%28x%29+for+x%3D%28-1%2C+1%29 tanh: http://www.wolframalpha.com/input/?i=plot+tanh%28x%29+for+x%3D%28-1%2C+1%29

, tanh y = 0,5 x = 0,5. x = 0,5 y = 0,62. , , , , , . , 0,5 0,62.

, . , . ., , http://luna.cas.usf.edu/~mbrannic/files/regression/Logistic.html http://www.cs.cmu.edu/~tom/mlbook/NBayesLogReg.pdf

Answer 2

{0,1}, .