On complexity of easy predictable sequences

Authors:
Michael V. Vyugin;Vladimir V. V'yugin
Affiliations:
Computer Learning Research Centre, Royal Holloway, University of London, Egham, Surrey, England;Insitute for Information Transmission Problems, Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, Moscow GSP-4, Russia/ and Computer Learning Research Centre, Royal Holloway, University of L ...
Venue:
Information and Computation
Year:
2002

Citing 11
Cited 1

Theory of recursive functions and effective computability

Theory of recursive functions and effective computability
Introduction to algorithms

Introduction to algorithms
Aggregating strategies

COLT '90 Proceedings of the third annual workshop on Computational learning theory
Randomized approximate aggregating strategies and their applications to prediction and discrimination

COLT '95 Proceedings of the eighth annual conference on Computational learning theory
How to use expert advice

Journal of the ACM (JACM)
An introduction to Kolmogorov complexity and its applications (2nd ed.)

An introduction to Kolmogorov complexity and its applications (2nd ed.)
Universal portfolio selection

COLT' 98 Proceedings of the eleventh annual conference on Computational learning theory
A game of prediction with expert advice

Journal of Computer and System Sciences - Special issue on the eighth annual workshop on computational learning theory, July 5–8, 1995
Most sequences are stochastic

Information and Computation
Non-linear Inequalities between Predictive and Kolmogorov Complexities

ALT '01 Proceedings of the 12th International Conference on Algorithmic Learning Theory
TIGHT WORST-CASE LOSS BOUNDS FOR PREDICTING WITH EXPERT ADVICE

TIGHT WORST-CASE LOSS BOUNDS FOR PREDICTING WITH EXPERT ADVICE

Predictive complexity and information

Journal of Computer and System Sciences - Special issue on COLT 2002

Quantified Score

Hi-index	0.00

Visualization

Abstract

Predictive complexity is a generalization of Kolmogorov complexity. It corresponds to an "optimal" prediction strategy and gives a natural lower bound to ability of any algorithm to predict elements of a sequence of outcomes. A natural question is studied: how complex can easy-to-predict sequences be? The standard measure of complexity, used in the paper, is Kolmogorov complexity K (which is close to predictive complexity for logarithmic loss function). The difficulty of prediction is measured by the notion of predictive complexity KG for bounded loss function (of nonlogarithmic type). We present an asymptotic relation sup x:l(x)=nK(x|n)/KG(x) ∼ 1/a log n, when n → ∞, where a is a constant and l(x) is the length of a sequence x. An analogous asymptotic relation holds for relative complexities K(x | n)/n and KG(x)/n, where n = l(x). To obtain these results we present lower and upper bounds of the cardinality of all sequences of given predictive complexity.