Stochastic chains with memory of variable length

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.

17 pages

References in corpus (1)

• Random perturbations of stochastic chains with unbounded variable length memory

Cited by in corpus (12)

• Context tree selection and linguistic rhythm retrieval from written texts
• Neighborhood radius estimation in Variable-neighborhood Random Fields
• Variable length Markov chains and dynamical sources
• Modeling networks of spiking neurons as interacting processes with memory of variable length
• Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes
• Context tree selection for functional data
• On the mathematical consequences of binning spike trains
• SeqROCTM: A Matlab toolbox for the analysis of Sequence of Random Objects driven by Context Tree Models
• Uncommon Suffix Tries
• Suficient conditions of standardness for filtrations of stationary processes taking values in a finite space
• Markov and almost Markov properties in one, two or more directions
• Stochastically Perturbed Chains of Variable Memory