Exponential inequalities for empirical unbounded context trees

TL;DR

This paper derives exponential convergence bounds for the Context algorithm applied to unbounded context trees, leading to strong consistency results and generalizing previous findings in variable length Markov chain estimation.

Contribution

It provides the first non-uniform exponential bounds for the Context algorithm on unbounded trees, enhancing understanding of its convergence properties.

Findings

Established exponential upper bounds for convergence rate

Proved strong consistency of the Context algorithm in unbounded settings

Generalized previous results to broader classes of trees

Abstract

In this paper we obtain non-uniform exponential upper bounds for the rate of convergence of a version of the algorithm Context, when the underlying tree is not necessarily bounded. The algorithm Context is a well-known tool to estimate the context tree of a Variable Length Markov Chain. As a consequence of the exponential bounds we obtain a strong consistency result. We generalize in this way several previous results in the field.