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

@article{Brgge2021OnTC, title={On the convergence of the Metropolis algorithm with fixed-order updates for multivariate binary probability distributions}, author={Kai Br{\"u}gge and Asja Fischer and C. Igel}, journal={ArXiv}, year={2021}, volume={abs/2006.14999} }

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…

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