Non-regular g-measures and variable length memory chains

Stochastic chains with memory of variable length

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 compres...

Variable Length Markov Chains

We study estimation in the class of stationary variable length Markov Ž . chains VLMC on a finite space. The processes in this class are still Markovian of high order, but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary highorder Markov chains. From an algorithmic view, the VLMC model class has attracted interest in information theory ...

Random Perturbations of Stochastic Chains with Unbounded Variable Length Memory

Abstract. We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequ...

Learning Variable Memory Length Markov Chains from Noisy Output

Variable length Markov chains and dynamical sources

Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sources is studied. We establish a probabilistic frame for context trees and VLMC and we prove that any VLMC is a dynamical source for which we explicitly build th...