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Is there a general goodness-of-fit test for any kind of regression model? My problem is that I have a deep neural network that tries to predict some real value labels using high-dimensional input. The loss function is not simply MSE but rather customized to incorporate some domain knowledge. I really want to test whether my model explains the data enough, or is not any better than random guess.

I know in linear regression there is R squared. Is there any similar metric but more general?

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