Uncertainty in Artificial Intelligence
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MCMC for doubly-intractable distributions
Iain Murray, Zoubin Ghahramani, David MacKay
Abstract:
Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are additional parameter-dependent normalization terms; for example, the posterior over parameters of an undirected graphical model. An ingenious auxiliary-variable scheme (Moeller et al., 2004) offers a solution: exact sampling (Propp and Wilson, 1996) is used to sample from a Metropolis-Hastings proposal for which the acceptance probability is tractable. Unfortunately the acceptance probability of these expensive updates can be low. This paper provides a generalization of Moeller et al. (2004) and a new MCMC algorithm, which obtains better acceptance probabilities for the same amount of exact sampling, and removes the need to estimate model parameters before sampling begins.
Keywords:
Pages: 359-366
PS Link:
PDF Link: /papers/06/p359-murray.pdf
BibTex:
@INPROCEEDINGS{Murray06,
AUTHOR = "Iain Murray and Zoubin Ghahramani and David MacKay",
TITLE = "MCMC for doubly-intractable distributions",
BOOKTITLE = "Proceedings of the Twenty-Second Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-06)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2006",
PAGES = "359--366"
}


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