Towards derandomising Markov chain Monte Carlo

We present a new framework to derandomise certain Markov chain Monte Carlo (MCMC) algorithms. As in MCMC, we first reduce counting problems to sampling from a sequence of marginal distributions. For the latter task, we introduce a method called coupling towards the past that can, in logarithmic time...

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Bibliographic Details
Published in:Proceedings / annual Symposium on Foundations of Computer Science pp. 1963 - 1990
Main Authors: Feng, Weiming, Guo, Heng, Wang, Chunyang, Wang, Jiaheng, Yin, Yitong
Format: Conference Proceeding
Language:English
Published: IEEE 06.11.2023
Subjects:
approximate counting
Approximation algorithms
Computer science
Couplings
deterministic algorithm
Markov chain Monte Carlo
Markov processes
Monte Carlo methods
Task analysis
ISSN:2575-8454
Online Access:Get full text
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Summary:We present a new framework to derandomise certain Markov chain Monte Carlo (MCMC) algorithms. As in MCMC, we first reduce counting problems to sampling from a sequence of marginal distributions. For the latter task, we introduce a method called coupling towards the past that can, in logarithmic time, evaluate one or a constant number of variables from a stationary Markov chain state. Since there are at most logarithmic random choices, this leads to very simple derandomisation. We provide two applications of this framework, namely efficient deterministic approximate counting algorithms for hypergraph independent sets and hypergraph colourings, under local lemma type conditions matching, up to lower order factors, their state-of-the-art randomised counterparts.
ISSN:2575-8454
DOI:10.1109/FOCS57990.2023.00120