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When using neural network for regression problems, the standard approach is to use tanh for hidden layer activation and linear or tanh for output layer activation.

The tanh function returns (-1, 1) and looks like the graph in the link below.

https://datascience.stackexchange.com/questions/14349/difference-of-activation-functions-in-neural-networks-in-general

The response variable in the problem I'm looking at has high kurtosis. So the response variable looks like the tanh graph rotated around the diagonal. i.e., for tanh, as x increases, y approaches 1 but never reach 1. My response variable is the other way around even after standardizing (i.e., (x - mean(x)) / std(x)), as x increases, y increases exponentially.

In this context, the linear function seems to provide a better fit than tanh. What would be a good candidate for the activation function?

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