Instytut Podstawowych Problemów Techniki
Polskiej Akademii Nauk

Partnerzy

dr hab. Łukasz Dębowski

Institute of Computer Science (PL)
Promotor prac doktorskich
1.  2020-10-15 Steifer Tomasz
(Instytut Podstaw Informatyki PAN)
Computable prediction of infinite binary sequences with zero one loss 

Ostatnie publikacje
1.  Dębowski Ł., Steifer T., UNIVERSAL CODING AND PREDICTION ON ERGODIC RANDOM POINTS, Bulletin of Symbolic Logic, ISSN: 1079-8986, DOI: 10.1017/bsl.2022.18, Vol.28, No.3, pp.387-412, 2022

Streszczenie:
Suppose that we have a method which estimates the conditional probabilities of some unknown stochastic source and we use it to guess which of the outcomes will happen. We want to make a correct guess as often as it is possible. What estimators are good for this? In this work, we consider estimators given by a familiar notion of universal coding for stationary ergodic measures, while working in the framework of algorithmic randomness, i.e., we are particularly interested in prediction of Martin-Löf random points. We outline the general theory and exhibit some counterexamples. Completing a result of Ryabko from 2009 we also show that universal probability measure in the sense of universal coding induces a universal predictor in the prequential sense. Surprisingly, this implication holds true provided the universal measure does not ascribe too low conditional probabilities to individual symbols. As an example, we show that the Prediction by Partial Matching (PPM) measure satisfies this requirement with a large reserve.

Słowa kluczowe:
algorithmic randomness, stationary ergodic processes, universal coding, universal prediction, prediction by partial matching

Afiliacje autorów:
Dębowski Ł. - IPPT PAN
Steifer T. - IPPT PAN
100p.

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