Statistical Windows in Testing for the Initial Distribution of a Reversible Markov Chain

6 Aug 2018Quentin BerthetVarun Kanade

We study the problem of hypothesis testing between two discrete distributions, where we only have access to samples after the action of a known reversible Markov chain, playing the role of noise. We derive instance-dependent minimax rates for the sample complexity of this problem, and show how its dependence in time is related to the spectral properties of the Markov chain... (read more)

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