Zonotope Hitandrun for Efficient Sampling from Projection DPPs
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:12231232, 2017.
Abstract
Determinantal point processes (DPPs) are distributions over sets of items that model diversity using kernels. Their applications in machine learning include summary extraction and recommendation systems. Yet, the cost of sampling from a DPP is prohibitive in largescale applications, which has triggered an effort towards efficient approximate samplers. We build a novel MCMC sampler that combines ideas from combinatorial geometry, linear programming, and Monte Carlo methods to sample from DPPs with a fixed sample cardinality, also called projection DPPs. Our sampler leverages the ability of the hitandrun MCMC kernel to efficiently move across convex bodies. Previous theoretical results yield a fast mixing time of our chain when targeting a distribution that is close to a projection DPP, but not a DPP in general. Our empirical results demonstrate that this extends to sampling projection DPPs, i.e., our sampler is more sampleefficient than previous approaches which in turn translates to faster convergence when dealing with costlytoevaluate functions, such as summary extraction in our experiments.
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