Some properties of sequential predictors for binary Markov sources

Neri Merhav*, Meir Feder, Michael Gutman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Universal prediction of the next outcome of a binary sequence drawn from a Markov source with unknown parameters is considered. For a given source, the predictability is defined as the least attainable expected fraction of prediction errors. A lower bound is derived on the maximum rate at which the predictability is asymptotically approached uniformly over all sources in the Markov class. This bound is achieved by a simple majority predictor. For Bernoulli sources, bounds on the large deviations performance are investigated. A lower bound is derived for the probability that the fraction of errors will exceed the predictability by a prescribed amount Δ > 0. This bound is achieved by the same predictor if Δ is sufficiently small.

Original languageEnglish
Pages (from-to)887-892
Number of pages6
JournalIEEE Transactions on Information Theory
Volume39
Issue number3
DOIs
StatePublished - May 1993
Externally publishedYes

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