Log In Sign Up

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

by   Kai Brügge, et al.

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 were they actually behave differently. If the standard algorithm also converges, the modified operator exhibits similar (if not better) performance in terms of convergence speed.


page 1

page 2

page 3

page 4


Reversible Genetically Modified Mode Jumping MCMC

In this paper, we introduce a reversible version of a genetically modifi...

Accelerating MCMC algorithms through Bayesian Deep Networks

Markov Chain Monte Carlo (MCMC) algorithms are commonly used for their v...

Quantum-enhanced Markov chain Monte Carlo

Sampling from complicated probability distributions is a hard computatio...

Stochastic Stein Discrepancies

Stein discrepancies (SDs) monitor convergence and non-convergence in app...

Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Net

We propose a novel method to directly learn a stochastic transition oper...

A Fast MCMC for the Uniform Sampling of Binary Matrices with Fixed Margins

Uniform sampling of binary matrix with fixed margins is an important and...

Discrete Network Dynamics. Part 1: Operator Theory

An operator algebra implementation of Markov chain Monte Carlo algorithm...