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Exact sampling of determinantal point processes without eigendecomposition

Part of: Stochastic processes

Published online by Cambridge University Press:  23 November 2020

Claire Launay Open the ORCID record for Claire Launay [Opens in a new window] ,
Bruno Galerne  and
Agnès Desolneux
Claire Launay*
Affiliation:
Université de Paris
Bruno Galerne*
Affiliation:
Université d’Orléans
Agnès Desolneux*
Affiliation:
CNRS and ENS Paris-Saclay
*
*Postal address: Laboratoire MAP5, Université de Paris, CNRS, Paris, 75006, France. Email: claire.launay.math@gmail.com
**Postal address: Institut Denis Poisson, Université d’Orléans, Université de Tours, CNRS, Orléans, 45100, France.
***Postal address: Centre Borelli, CNRS, ENS Paris Saclay, Gif-sur-Yvette, 91190, France.
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Abstract

Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel K that can be seen, in a discrete setting, as a matrix storing the similarity between points. The main exact algorithm to sample DPPs uses the spectral decomposition of K, a computation that becomes costly when dealing with a high number of points. Here we present an alternative exact algorithm to sample in discrete spaces that avoids the eigenvalues and the eigenvectors computation. The method used here is innovative, and numerical experiments show competitive results with respect to the initial algorithm.

Keywords

Determinantal point processexact samplingthinningCholesky decompositiongeneral marginal

MSC classification

Primary: 68U20: Simulation
Secondary: 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 4 , December 2020 , pp. 1198 - 1221
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Copyright
© Applied Probability Trust 2020

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