Invited Speaker - Aurélien Garivier (CNRS/ENST)

Title:

Context trees and source coding .

Abstract:

Context tree probability sources are flexible stochastic processes generalizing Markov chains: the distribution of a variable X_k depends on a finite but not necessarily constant number of past variables X_{k-1}, X_{k-2},... In this presentation, some applications of the context models to source coding are discussed. Source coding can be interpreted as a particular problem of density estimation with logarithmic loss. Two approaches are presented : first, context tree estimation procedures (Rissanen's Context algorithm and Penalized Maximum Likelihood); second, a fully Bayesian procedure called Context Tree Weighting, involving a double mixture of context tree models. It appears that context trees prove unexpectedly useful even for long-memory processes.