Research
On two ways to use determinantal point processes for Monte Carlo integration
arXiv:2604.19698v1 Announce Type: new Abstract: The standard Monte Carlo estimator widehat{I}_N^{MC} of int fdomega relies on independent samples from omega and has variance of order 1/N. Replacing th
arXiv:2604.19698v1 Announce Type: new Abstract: The standard Monte Carlo estimator widehat{I}_N^{MC} of int fdomega relies on independent samples from omega and has variance of order 1/N. Replacing the samples with a determinantal point process (DPP), a repulsive distribution, makes the estimator consistent, with variance rates that depend on how the DPP is adapted to f and omega. We examine two existing DPP-based estimators: one by Bardenet & Hardy (2020) with a rate of O(N^{-(1+1/d)}) for smooth f, but relying on a fixed DPP. The other, by Ermakov & Zolotukhin (1960), is unbiased with rate of order 1/N, like Monte Carlo, but its DPP is tailored to f. We revisit these estimators, generalize them to continuous settings, and provide sampling algorithms.
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Source: arXiv cs.LG | 2026-04-22