Continuous Relaxations for Discrete Hamiltonian Monte Carlo
NIPS(2012)
摘要
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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关键词
Discrete system,Continuous modelling,Discrete optimization,Hybrid Monte Carlo,Inference,Gaussian integral,Partition function (mathematics),Applied mathematics,Normalization (statistics),Mathematical optimization,Mathematics
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