Abstract

Continuous relaxations play an important role in discrete optimization, but havenot seen much use in approximate probabilistic inference. Here we show that ageneral form of the Gaussian Integral Trick makes it possible to transform a wideclass of discrete variable undirected models into fully continuous systems. Thecontinuous representation allows the use of gradient-based Hamiltonian MonteCarlo 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 continuousrelaxation inference algorithms on a number of illustrative problems.

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