On two ways to use determinantal point processes for Monte Carlo integration
2019 · in (NeurIPS 2019) and (ICML 2019 - NEGDEP)
Abstract
When approximating an integral by a weighted sum of function evaluations, determinantal point processes (DPPs) provide a way to enforce repulsion between the evaluation points. We analyze the Ermakov-Zolotukhin estimator using modern arguments and provide an efficient implementation to sample exactly a particular multidimensional DPP called multivariate Jacobi ensemble. We investigate the behavior of two unbiased Monte Carlo estimators and demonstrate good properties when the kernel is adapted to a basis in which the integrand is sparse or has fast-decaying coefficients.
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