An Efficient Bayes Coding Algorithm for the Non-Stationary Source in Which Context Tree Model Varies from Interval to Interval

Abstract

The context tree source is a source model in which the occurrence probability of symbols is determined from a finite past sequence, and is a broader class of sources that includes i.i.d. and Markov sources. This paper proposes a source model such that its subsequence is generated from a different context tree model. The Bayes code for such sources requires weighting of the posterior probability distributions for the change patterns of the context tree source and all possible context tree models. Therefore, the challenge is how to reduce this exponential order computational complexity. In this paper, we assume a special class of prior probability distribution of change patterns and context tree models, and propose an efficient Bayes coding algorithm whose computational complexity is the polynomial order. A full version of this paper is accessible at: https://arxiv.org/abs/2105.05163