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I have a regression problem where I am predicting a continuous variable. Loss functions used most often in these cases (RMSE, MAE, etc.) don't treat over- or under- predictions differently.

I am in a scenario where under-predicting would be a much worse outcome than over-predicting.

What type of loss function would appropriately capture this?

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    $\begingroup$ Use something like RMSE but multiply by alpha > 1 if it's an under prediction and by 0 < beta < 1 if it's an over prediction? $\endgroup$
    – kbrose
    Sep 8, 2017 at 14:06
  • $\begingroup$ Can the business cost of failed predictions be made explicit in your case? You might be able to make your business cost per example (or a transformation of it) the loss function, instead of a test metric. $\endgroup$ Sep 8, 2017 at 16:22
  • $\begingroup$ I'm not sure what 'under-' and 'over-' predictions are, but if you mean that your data is unbalanced towards a certain class, I suggest using Infogain Loss matrix to counter that $\endgroup$
    – Alex
    Sep 12, 2017 at 17:10

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Pick an asymmetric loss function. One option is quantile regression (linear but with different slopes for positive and negative errors).

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