Minimum Description Length Principle for Maximum Entropy Model Selection

Abstract: Model selection is central to statistics, and many learning problems can be formulated as model selection problems. In this paper, we treat the problem of selecting a maximum entropy model given various feature subsets and their moments, as a model selection problem, and present a minimum description length (MDL) formulation to solve this problem. For this, we derive normalized maximum likelihood (NML) codelength for these models. Furthermore, we prove that the minimax entropy principle is a special case of maximum entropy model selection, where one assumes that complexity of all the models are equal. We apply our approach to gene selection problem and present simulation results.