Abstract
We consider the problem of estimating from sample paths the absolute spectral gap 1 - λ of a reversible, irreducible and aperiodic Markov chain (Xt )t€N over a finite state space Ω. We propose the UCPI (Upper Confidence Power Iteration) algorithm for this problem, a low-complexity algorithm which estimates the spectral gap in time O(n) and memory space O((lnn)2) given n samples. This is in stark contrast with most known methods which require at least memory space O((ln n)2), so that they cannot be applied to large state spaces. Furthermore, UCPI is amenable to parallel implementation.
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