Takeuchi's Information Criterion (TIC) was introduced as a generalization of Akaike's Information Criterion (AIC) in 1976. Though TIC avoids many of AIC's strict requirements and assumptions, it is only rarely used. One of the reasons for this is that the trace term introduced in TIC is numerically unstable and computationally expensive to compute. An extension of TIC called ICE was published in 2021, which allows this trace term to be used for model fitting (where it was primarily compared to L2 regularization) instead of just model selection. That paper also examined numerically stable and computationally efficient approximations that could be applied to TIC or ICE, but these approximations were only examined on small synthetic models. This paper applies and extends these approximations to larger models on real datasets for both TIC and ICE. This work shows the practical models may use TIC and ICE in a numerically stable way to achieve superior results at a reasonable computational cost.
Keywords: AIC; ICE; TIC; entropy; generalization error; information criteria; overfitting.