Hyperparameter Learning of Bayesian Context Tree Models

Yuta Nakahara, Shota Saito, Koshi Shimada, Toshiyasu Matsushima

Abstract: In recent years, Bayesian counterparts of the context tree weighting method are studied for many tasks. All these tasks require a hyperparameter setting of the prior distribution for context tree models. Therefore, we provide a framework for statistically learning these hyperparameters from data. Specifically, we consider a hierarchical Bayesian model that assumes hyperprior distributions behind the hyperparameters and learn them using an empirical variational Bayesian (EVB) method. This is the first study to propose an EVB method on the Bayesian context trees. The derived algorithm has a suggestive form that consists of subroutines partially optimal to each local probabilistic model.