Minimax Testing of Identity to a Reference Ergodic Markov Chain

Geoffrey Wolfer, Aryeh Kontorovich

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

Abstract

We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or e-far from a given reference chain. We obtain nearly matching (up to logarithmic factors) upper and lower sample complexity bounds for our notion of distance, which is based on total variation. Perhaps surprisingly, we discover that the sample complexity depends solely on the properties of the known reference chain and does not involve the unknown chain at all, which is not even assumed to be ergodic.
Original languageEnglish GB
Title of host publicationProceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics
EditorsSilvia Chiappa, Roberto Calandra
PublisherPMLR
Pages191-201
Number of pages11
Volume108
StatePublished - 2020

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR

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