Markov Chain Truncation for DoublyIntractable Inference
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Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:776784, 2017.
Abstract
Computing partition functions, the normalizing constants of probability distributions, is often hard. Variants of importance sampling give unbiased estimates of a normalizer Z, however, unbiased estimates of the reciprocal 1/Z are harder to obtain. Unbiased estimates of 1/Z allow Markov chain Monte Carlo sampling of “doublyintractable” distributions, such as the parameter posterior for Markov Random Fields or Exponential Random Graphs. We demonstrate how to construct unbiased estimates for 1/Z given access to blackbox importance sampling estimators for Z. We adapt recent work on random series truncation and Markov chain coupling, producing estimators with lower variance and a higher percentage of positive estimates than before. Our debiasing algorithms are simple to implement, and have some theoretical and empirical advantages over existing methods.
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