The mean square error squares the error as a result all the errors become positive. The information pertaining to the positivity or negetivity of the error is lost. Are there any error functions that take into account the sign of the error?
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This is not really a programming question. I think it's better suited for [stats.se]. – Jan 08 '15 at 05:14
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You can design a model-specific loss function if you want to penalize underestimations more than overestimations (and vice versa) or even to tolerate some underestimations.
This can be achieved with the help of piecewise-linear loss function, for example. Then you'll have to use some (sub)gradient optimization routine in order to learn a model.
Artem Sobolev
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@Shaun, variations of gradient descent: AdaGrad, Nesterov's accelerated Method, Momentum, and many others. – Artem Sobolev Jan 09 '15 at 08:12