Open Access
2021 On universal algorithms for classifying and predicting stationary processes
Gusztáv Morvai, Benjamin Weiss
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Probab. Surveys 18: 77-131 (2021). DOI: 10.1214/20-PS345


This is a survey of results on universal algorithms for classification and prediction of stationary processes. The classification problems include discovering the order of a k-step Markov chain, determining memory words in finitarily Markovian processes and estimating the entropy of an unknown process. The prediction problems cover both discrete and real valued processes in a variety of situations. Both the forward and the backward prediction problems are discussed with the emphasis being on pointwise results. This survey is just a teaser. The purpose is merely to call attention to results on classification and prediction. We will refer the interested reader to the sources. Throughout the paper we will give illuminating examples.

Funding Statement

The first author was supported partly by the Alfréd Rényi Institute of Mathematics, the Bolyai János Research Scholarship and OTKA grant No. K75143.


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Gusztáv Morvai. Benjamin Weiss. "On universal algorithms for classifying and predicting stationary processes." Probab. Surveys 18 77 - 131, 2021.


Received: 1 May 2020; Published: 2021
First available in Project Euclid: 16 April 2021

Digital Object Identifier: 10.1214/20-PS345

Primary: 60G10 , 60G25

Keywords: Prediction theory , Stationary processes

Vol.18 • 2021
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