Improving the Performance and Stability of TIC and ICE

Area of Science:

• Statistics
• Machine Learning
• Econometrics

Background:

• Akaike's Information Criterion (AIC) has limitations.
• Takeuchi's Information Criterion (TIC), a 1976 AIC generalization, is underutilized due to computational challenges with its trace term.
• The Information Criterion Extension (ICE) was proposed in 2021 to address some TIC limitations.

Purpose of the Study:

• To apply and extend numerically stable and computationally efficient approximations for TIC and ICE.
• To evaluate these approximations on larger, real-world datasets.
• To demonstrate the practical viability of TIC and ICE for model fitting and selection.

Main Methods:

• Implementation of previously proposed approximations for TIC and ICE.
• Extension of these approximations to handle larger models.
• Validation on real-world datasets, comparing performance and computational cost.

Main Results:

• The study successfully applied and extended approximations for TIC and ICE to large, real-world models.
• Numerically stable and computationally efficient methods for utilizing TIC and ICE were demonstrated.
• Achieved superior results in practical model fitting using these enhanced criteria.

Conclusions:

• TIC and ICE can be practically implemented in a numerically stable manner.
• These methods offer superior results for model fitting at a reasonable computational cost.
• The findings encourage wider adoption of TIC and ICE in statistical modeling and machine learning.