TY - GEN

T1 - Universal prediction of individual sequences

AU - Feder, Meir

AU - Merhav, Neri

AU - Gutman, Michael

N1 - Publisher Copyright:
© Proceedings - 17th Convention of Electrical and Electronics Engineers in Israel, EEIS 1991. All rights reserved.

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85067605630&partnerID=8YFLogxK

U2 - 10.1109/EEIS.1991.217658

DO - 10.1109/EEIS.1991.217658

M3 - פרסום בספר כנס

AN - SCOPUS:85067605630

T3 - Proceedings - 17th Convention of Electrical and Electronics Engineers in Israel, EEIS 1991

SP - 223

EP - 226

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

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 5 March 1991 through 7 March 1991

ER -