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Continuous Relaxations for Discrete Hamiltonian Monte Carlo

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http://books.nips.cc/papers/files/nips25/NIPS2012_1464.pdf
Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 25
Subtitle of host publication26th Annual Conference on Neural Information Processing Systems 2012. Proceedings of a meeting held December 3-6, 2012, Lake Tahoe, Nevada, United States
PublisherMIT Press
Pages3203-3211
Number of pages9
Publication statusPublished - 2012

Abstract

Continuous relaxations play an important role in discrete optimization, but have not seen much use in approximate probabilistic inference. Here we show that a general form of the Gaussian Integral Trick makes it possible to transform a wide class of discrete variable undirected models into fully continuous systems. The continuous representation allows the use of gradient-based Hamiltonian Monte Carlo for inference, results in new ways of estimating normalization constants (partition functions), and in general opens up a number of new avenues for inference in difficult discrete systems. We demonstrate some of these continuous relaxation inference algorithms on a number of illustrative problems.

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