On Two Ways to use Determinantal Point Processes for Monte Carlo Integration

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 inter- est: 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 multidimensional DPP called multivariate Jacobi ensemble. This let us investigate the behavior of both estimators on toy problems in yet unexplored regimes.