Zonotope hit-and-run for efficient sampling from projection DPPs

Guillaume Gautier 1, 2, 3 Rémi Bardenet 2, 3 Michal Valko 1
1 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
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 large-scale 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 hit-and-run 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 sample-efficient than previous approaches which in turn translates to faster convergence when dealing with costly-to-evaluate functions, such as summary extraction in our experiments.
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Communication dans un congrès
International Conference on Machine Learning, 2017, Sydney, Australia
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Contributeur : Michal Valko <>
Soumis le : mardi 13 juin 2017 - 02:57:10
Dernière modification le : mardi 3 juillet 2018 - 11:27:16
Document(s) archivé(s) le : mardi 12 décembre 2017 - 11:49:33


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  • HAL Id : hal-01526577, version 2


Guillaume Gautier, Rémi Bardenet, Michal Valko. Zonotope hit-and-run for efficient sampling from projection DPPs. International Conference on Machine Learning, 2017, Sydney, Australia. 〈hal-01526577v2〉



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