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Pretty simple question here:
Is it useful to use the standard deviation, skew, kurtosis, or any other extrapolatory stats as features, and if so in which problem sets?
In this case, I am talking about deep learning problems.
I would say it is useful if you have an extensive knowledge in the domain you want to apply your model in. You also need more data for it to yield reasonable results.
As for real world uses l can only think of trading at the moment.