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Sampling from a k-DPP without looking at all items

Daniele Calandriello 1 Michał Dereziński 2 Michal Valko 1, 3 
3 Scool - Scool
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : Determinantal point processes (DPPs) are a useful probabilistic model for selecting a small diverse subset out of a large collection of items, with applications in summarization, stochastic optimization, active learning and more. Given a kernel function and a subset size k, our goal is to sample k out of n items with probability proportional to the determinant of the kernel matrix induced by the subset (a.k.a. k-DPP). Existing k-DPP sampling algorithms require an expensive preprocessing step which involves multiple passes over all n items, making it infeasible for large datasets. A naïve heuristic addressing this problem is to uniformly subsample a fraction of the data and perform k-DPP sampling only on those items, however this method offers no guarantee that the produced sample will even approximately resemble the target distribution over the original dataset. In this paper, we develop α-DPP, an algorithm which adaptively builds a sufficiently large uniform sample of data that is then used to efficiently generate a smaller set of k items, while ensuring that this set is drawn exactly from the target distribution defined on all n items. We show empirically that our algorithm produces a k-DPP sample after observing only a small fraction of all elements, leading to several orders of magnitude faster performance compared to the state-of-the-art. Our implementation of α-DPP is provided at https://github.com/guilgautier/DPPy/.
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https://hal.inria.fr/hal-03287832
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Submitted on : Thursday, July 15, 2021 - 9:50:23 PM
Last modification on : Sunday, June 26, 2022 - 9:10:13 AM
Long-term archiving on: : Saturday, October 16, 2021 - 7:17:25 PM

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Daniele Calandriello, Michał Dereziński, Michal Valko. Sampling from a k-DPP without looking at all items. Neural Information Processing Systems, 2020, Montréal, Canada. ⟨hal-03287832⟩

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