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

arXiv: https://arxiv.org/abs/2604.19698 · HTML: https://mlsanity.com/paper/2604.19698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 21 Apr 2026.

## Builds on (most cited first, 7 of 7)

- [On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions](https://mlsanity.com/paper/1502.06800/) (2015)
- [Control functionals for Monte Carlo integration](https://mlsanity.com/paper/1410.2392/) (2014)
- [Monte Carlo with Determinantal Point Processes](https://mlsanity.com/paper/1605.00361/) (2016)
- [Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees](https://mlsanity.com/paper/1506.02681/) (2015)
- [Black-box Importance Sampling](https://mlsanity.com/paper/1610.05247/) (2016)
- [Fast determinantal point processes via distortion-free intermediate sampling](https://mlsanity.com/paper/1811.03717/) (2018)
- [Exact Sampling of Determinantal Point Processes without Eigendecomposition](https://mlsanity.com/paper/1802.08429/) (2018)

## Abstract (arXiv)

The standard Monte Carlo estimator widehatINMC of int fdω relies on independent samples from ω 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 ω. 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.