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MCMC for doubly-intractable distributions

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Markov chain Monte Carlo (MCMC) is a well-established framework for sampling from complex probability distributions. However, standard MCMC algorithms cannot sample from “doubly-intractable” distributions. Doubly-intractable distributions include the posterior over parameters of many undirected graphical models and some point-process models. Every step of a Markov chain seems to require the computation of an intractable normalization term.

There are a growing number of valid MCMC algorithms for doubly-intractable distributions. They all involve daunting computations, but at least give insight into the problem. I will review what is possible and the implications for the Bayesian learning of undirected graphical models.

If time allows I will share a recent insight by Ryan Adams, which combined with MCMC algorithms for doubly-intractable distributions, allows Bayesian density estimation using Gaussian Processes.

This is work with David MacKay, Zoubin Ghahramani and Ryan Adams.

This talk is part of the Statistics series.

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