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My data is gamma distributed (clearly skewed to the right) but when I use the log link function the distribution that my model is producing is Gaussian. Not sure why. Any thoughts appreciated!
Very helpful answer. I was wondering why in DL models, which are inherently nonlinear it still makes sense to use MSE as loss for regression models. The assumption must be that errors are still normally distributed. This, of course, isn’t always the case. For example, in insurance claim frequency models we assume the target is Poisson distributed and so the errors are not normally distributed. Therefore, we would use Poisson deviance or loss instead of MSE.
I have wondered the same thing. The MSE is derived from the assumptions made for linear regression namely that the errors are normally distributed. Clearly the neural network regression models are not limited to these assumptions…far from it as the point is to handle non-linearity quite explicitly. And yet we use MSE still.
@NickCox I'm curious how you consider classification as a limiting case of regression. In regression the order of the target variable matters but in classification it does not. I can reverse the labels and it is still the same problem. What we call the target is irrelevant. That is not true for regression problems where the actual target is important to keep track of.
One way I can imagine time being a covariate (as opposed to just an offset) is if somehow playing time is an indicator of shooting quality (eg players that play more minutes shoot better). If we assume playing time does not reflect anything about the quality of shooting, then pure offset makes sense. For example, in this case it is not that the player necessarily even plays more, but just how much we observed the player.
