Isn't AIC just an approximation to cross-entropy, in the simplest possible case of gaussian noise? It's a rule of thumb which is useful in much simpler cases (a

Isn't AIC just an approximation to cross-entropy, in the simplest possible case of gaussian noise? It's a rule of thumb which is useful in much simpler cases (a few parameters, lots of data) than typical for say neural nets. Not the optimal reference, but a paper dealing with deriving AIC like this which I happen to have on my desk: Gelman & co 2014 https://link.springer.com/article/10.1007/s11222-013-9416-2 https://link.springer.com/article/10.1007/s11222-013-9416-2