On the convergence of the Metropolis algorithm with fixed-order updates for multivariate binary probability distributions.

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt


The Metropolis algorithm is arguably the most fundamental Markov chain Monte Carlo (MCMC) method. But the algorithm is not guaranteed to converge to the desired distribution in the case of multivariate binary distributions (e.g., Ising models or stochastic neural networks such as Boltzmann machines) if the variables (sites or neurons) are updated in a fixed order, a setting commonly used in practice. The reason is that the corresponding Markov chain may not be irreducible. We propose a modified Metropolis transition operator that behaves almost always identically to the standard Metropolis operator and prove that it ensures irreducibility and convergence to the limiting distribution in the multivariate binary case with fixed-order updates. The result provides an explanation for the behaviour of Metropolis MCMC in that setting and closes a long-standing theoretical gap. We experimentally studied the standard and modified Metropolis operator for models where they actually behave differently. If the standard algorithm also converges, the modified operator exhibits similar (if not better) performance in terms of convergence speed.
TitelProceedings of The 24th International Conference on Artificial Intelligence and Statistic
StatusUdgivet - 2021
Begivenhed24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021) - San Diego, USA
Varighed: 13 apr. 202115 apr. 2021


Konference24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021)
BySan Diego
NavnProceedings of Machine Learning Research

ID: 287826148