Universal prediction of individual sequences

Meir Feder, Neri Merhav, Michael Gutman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The problem of sequentially determining the next, future, outcome of a specific binary individual sequence, based on its observed past, using a finite state (FS), predictor is considered. We define the finite state predictability of the (infinite) sequence x1... xn..., as the minimum fraction of prediction errors that can be made by any FS predictor and prove that this fraction of errors can be achieved, upto an arbitrary small prescribed distance, for each individual sequence, by fully sequential guessing schemes. The rate at which the sequential guessing schemes approach the predictability is also calculated. Furthermore, we provide an efficient guessing procedure, based on the incremental parsing algorithm used in the Lempel-Ziv data compression method, and show that its fraction of errors also approaches the predictability of the sequence. Finally we discuss some relations between compressibility and predictability, and suggest to use the predictability as an additional measure for the complexity, or randomness, of the sequence.

Original languageEnglish
Title of host publicationProceedings - 17th Convention of Electrical and Electronics Engineers in Israel, EEIS 1991
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages223-226
Number of pages4
ISBN (Electronic)0879426780, 9780879426781
DOIs
StatePublished - 1991
Event17th Convention of Electrical and Electronics Engineers in Israel, EEIS 1991 - Tel Aviv, Israel
Duration: 5 Mar 19917 Mar 1991

Publication series

NameProceedings - 17th Convention of Electrical and Electronics Engineers in Israel, EEIS 1991

Conference

Conference17th Convention of Electrical and Electronics Engineers in Israel, EEIS 1991
Country/TerritoryIsrael
CityTel Aviv
Period5/03/917/03/91

Fingerprint

Dive into the research topics of 'Universal prediction of individual sequences'. Together they form a unique fingerprint.

Cite this