Intracluster Moves for Constrained DiscreteSpace MCMC
Firas Hamze, Nando de Freitas
Abstract:
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 Gaborlike filters as potentials, and a challenging threedimensional spinglass (with positive and negative potentials).
Keywords:
Pages: 236243
PS Link:
PDF Link: /papers/10/p236hamze.pdf
BibTex:
@INPROCEEDINGS{Hamze10,
AUTHOR = "Firas Hamze
and Nando de Freitas",
TITLE = "Intracluster Moves for Constrained DiscreteSpace MCMC",
BOOKTITLE = "Proceedings of the TwentySixth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI10)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2010",
PAGES = "236243"
}

