Intracluster Moves for Constrained Discrete-Space MCMC
It addresses sampling challenges in statistical physics and probabilistic inference, but it is incremental as it builds on existing MCMC methods for constrained binary distributions.
The paper tackles the problem of sampling from binary distributions with constraints, such as a fixed number of active variables, by proposing an MCMC method that allows large, energetically favorable moves. It demonstrates the algorithm on three Boltzmann machines, including a ferromagnetic Ising model, a restricted Boltzmann machine with learned filters, and a challenging spin-glass model.
This paper addresses the problem of sampling from binary distributions with constraints. In particular, it proposes an MCMC method to draw samples from a distribution of the set of all states at a specified distance from some reference state. For example, when the reference state is the vector of zeros, the algorithm can draw samples from a binary distribution with a constraint on the number of active variables, say the number of 1's. We motivate the need for this algorithm with examples from statistical physics and probabilistic inference. Unlike previous algorithms proposed to sample from binary distributions with these constraints, the new algorithm allows for large moves in state space and tends to propose them such that they are energetically favourable. The algorithm is demonstrated on three Boltzmann machines of varying difficulty: A ferromagnetic Ising model (with positive potentials), a restricted Boltzmann machine with learned Gabor-like filters as potentials, and a challenging three-dimensional spin-glass (with positive and negative potentials).