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Taming the Curse of Dimensionality: Discrete Integration by Hashing and Optimization

Stefano Ermon, Carla Gomes, Ashish Sabharwal, Bart Selman
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JMLR W&CP 28 (2) : 334–342, 2013

Abstract

Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a general discrete integral defined over an exponentially large set. This algorithm relies on solving only a small number of instances of a discrete combinatorial optimization problem subject to randomly generated parity constraints used as a hash function. As an application, we demonstrate that with a small number of MAP queries we can efficiently approximate the partition function of discrete graphical models, which can in turn be used, for instance, for marginal computation or model selection.

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