Minimax Testing of Identity to a Reference Ergodic Markov Chain
Machine Learning
2019-09-26 v3 Machine Learning
Statistics Theory
Statistics Theory
Abstract
We exhibit an efficient procedure for testing, based on a single long state sequence, whether an unknown Markov chain is identical to or -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.
Keywords
Cite
@article{arxiv.1902.00080,
title = {Minimax Testing of Identity to a Reference Ergodic Markov Chain},
author = {Geoffrey Wolfer and Aryeh Kontorovich},
journal= {arXiv preprint arXiv:1902.00080},
year = {2019}
}
Comments
A previous version of this print contained a mistake in a proof. We have now fixed it