For the 200+ n-gram models we evaluate, we find that the empirical relationship holds with a correlation of 0.9997 where γ is a constant and whereΛ = {λ i } are regularized parameter estimates; i.e., rather than estimating performance for maximum likelihood models as in AIC, we do this for regularized models.
test set cross-entropy can be approximated by the sum of the training set cross-entropy and the scaled sum of the magnitudes of the model parameters.