On two ways to use determinantal point processes for Monte Carlo integration

Guillaume Gautier 1, 2 R. Bardenet 1, 3 Michal Valko 2, 4
2 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : This paper focuses on Monte Carlo integration with determinantal point processes (DPPs) which enforce negative dependence between quadrature nodes. We survey the properties of two unbiased Monte Carlo estimators of the integral of interest: a direct one proposed by Bardenet & Hardy (2016) and a less obvious 60-year-old estimator by Ermakov & Zolotukhin (1960) that actually also relies on DPPs. We provide an efficient implementation to sample exactly a particular multidimen-sional DPP called multivariate Jacobi ensemble. This let us investigate the behavior of both estima-tors on toy problems in yet unexplored regimes.
Complete list of metadatas

Cited literature [15 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02160382
Contributor : Rémi Bardenet <>
Submitted on : Wednesday, June 19, 2019 - 3:46:25 PM
Last modification on : Friday, July 5, 2019 - 9:01:59 AM

File

icml_camera_ready.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02160382, version 1

Collections

Citation

Guillaume Gautier, R. Bardenet, Michal Valko. On two ways to use determinantal point processes for Monte Carlo integration. NEGDEPML 2019 - ICML Workshop on Negative Dependence in ML, Jun 2019, Long Beach, CA, United States. ⟨hal-02160382⟩

Share

Metrics

Record views

50

Files downloads

35