Ranking models for combination

A considerable amount of research has addressed the methods and objectives of model combination. Very little attention has been given to the question of how to obtain a good collection of models for combination. Here a rationale for inductive inference of multiple models of time series is developed in terms of algorithmic information theory. A model-based Kolmogorov sufficient statistic is described, and is utilized in a recursive scheme for ranking models in a population. Ranks are assigned in such a way that the n top-ranked models are considered to be the best subset of n models to use in combination. The ranking scheme is appropriate for use in the selection operation of an evolutionary computation. The treatment is primarily theoretical, but several practical issues in ranking and model combination are addressed.