Embed and Project: Discrete Sampling with Universal Hashing

Stefano Ermon, Carla P. Gomes, Ashish Sabharwal, Bart Selman
2013 Neural Information Processing Systems  
We consider the problem of sampling from a probability distribution defined over a high-dimensional discrete set, specified for instance by a graphical model. We propose a sampling algorithm, called PAWS, based on embedding the set into a higher-dimensional space which is then randomly projected using universal hash functions to a lower-dimensional subspace and explored using combinatorial search methods. Our scheme can leverage fast combinatorial optimization tools as a blackbox and, unlike
more » ... C methods, samples produced are guaranteed to be within an (arbitrarily small) constant factor of the true probability distribution. We demonstrate that by using state-of-the-art combinatorial search tools, PAWS can efficiently sample from Ising grids with strong interactions and from software verification instances, while MCMC and variational methods fail in both cases.
dblp:conf/nips/ErmonGSS13 fatcat:3sfucsgamzfrjick63y4cyeemy