Perfect Memory Context Trees in time series modeling

TL;DR

This paper explores perfect-memory context trees in time series modeling, providing combinatorial characterizations and an efficient algorithm to identify minimal perfect-memory extensions of stochastic context trees, enhancing the understanding of Markov Chain dependencies.

Contribution

It introduces the concept of perfect-memory context trees, offers combinatorial characterizations, and presents an efficient algorithm for minimal extension of stochastic context trees.

Findings

Characterization of perfect-memory context trees

Algorithm for minimal perfect-memory extension

Enhanced modeling of Markov dependencies

Abstract

The Stochastic Context Tree (SCOT) is a useful tool for studying infinite random sequences generated by an m-Markov Chain (m-MC). It captures the phenomenon that the probability distribution of the next state sometimes depends on less than m of the preceding states. This allows compressing the information needed to describe an m-MC. The SCOT construction has been earlier used under various names: VLMC, VOMC, PST, CTW. In this paper we study the possibility of reducing the m-MC to a 1-MC on the leaves of the SCOT. Such context trees are called perfect-memory. We give various combinatorial characterizations of perfect-memory context trees and an efficient algorithm to find the minimal perfect-memory extension of a SCOT.