Stochastic chains with memory of variable length

TL;DR

This paper introduces stochastic chains with variable-length memory, highlighting their theoretical foundation, applications across disciplines, and focusing on the Context algorithm and its convergence properties.

Contribution

It provides an accessible introduction to variable-length memory chains, emphasizing the Context algorithm and its convergence rate, bridging theory and practical applications.

Findings

The Context algorithm effectively models variable-length dependencies.

Convergence rate of the Context algorithm is characterized.

Applications span biology, linguistics, and music.

Abstract

Stochastic chains with memory of variable length constitute an interesting family of stochastic chains of infinite order on a finite alphabet. The idea is that for each past, only a finite suffix of the past, called context, is enough to predict the next symbol. These models were first introduced in the information theory literature by Rissanen (1983) as a universal tool to perform data compression. Recently, they have been used to model up scientific data in areas as different as biology, linguistics and music. This paper presents a personal introductory guide to this class of models focusing on the algorithm Context and its rate of convergence.