Intracluster Moves for Constrained Discrete-Space MCMC

Firas Hamze, Nando de Freitas
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:244-251, 2010.

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 refer- ence 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 in- ference. 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 dif- ficulty: A ferromagnetic Ising model (with positive potentials), a restricted Boltzmann machine with learned Gabor-like filters as po- tentials, and a challenging three-dimensional spin-glass (with positive and negative poten- tials).

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-hamze10a, title = {Intracluster Moves for Constrained Discrete-Space {MCMC}}, author = {Hamze, Firas and de Freitas, Nando}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {244--251}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/hamze10a/hamze10a.pdf}, url = {https://proceedings.mlr.press/r8/hamze10a.html}, 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 refer- ence 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 in- ference. 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 dif- ficulty: A ferromagnetic Ising model (with positive potentials), a restricted Boltzmann machine with learned Gabor-like filters as po- tentials, and a challenging three-dimensional spin-glass (with positive and negative poten- tials).}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Intracluster Moves for Constrained Discrete-Space MCMC %A Firas Hamze %A Nando de Freitas %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-hamze10a %I PMLR %P 244--251 %U https://proceedings.mlr.press/r8/hamze10a.html %V R8 %X 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 refer- ence 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 in- ference. 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 dif- ficulty: A ferromagnetic Ising model (with positive potentials), a restricted Boltzmann machine with learned Gabor-like filters as po- tentials, and a challenging three-dimensional spin-glass (with positive and negative poten- tials). %Z Reissued by PMLR on 04 October 2026.
APA
Hamze, F. & de Freitas, N.. (2010). Intracluster Moves for Constrained Discrete-Space MCMC. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:244-251 Available from https://proceedings.mlr.press/r8/hamze10a.html. Reissued by PMLR on 04 October 2026.

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