# Computationally Efficient Estimation of the Spectral Gap of a Markov Chain

@article{Combes2019ComputationallyEE,
title={Computationally Efficient Estimation of the Spectral Gap of a Markov Chain},
author={Richard Combes and Mikael Touati},
journal={Abstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems},
year={2019}
}
• Published 20 June 2019
• Mathematics, Computer Science
• Abstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems
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((ln n)2 given n samples. This is in stark contrast with most known methods which require at least memory space O(|Ω|), so that they cannot be…
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