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

TL;DR

This paper introduces an efficient Bayes coding algorithm for non-stationary sources modeled by varying context tree models, reducing computational complexity from exponential to polynomial order.

Contribution

It proposes a novel prior distribution and algorithm that significantly improves the computational efficiency of coding non-stationary context tree sources.

Findings

Achieves polynomial-time complexity for Bayes coding.

Effectively models sources with changing context tree structures.

Demonstrates practical applicability for non-stationary data compression.

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. The proposed source model in this paper represents that a subsequence in each interval 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 for 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.