# Nonparametric estimation of continuous DPPs with kernel methods

arXiv: https://arxiv.org/abs/2106.14210 · HTML: https://mlsanity.com/paper/2106.14210/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 27 Jun 2021.

## Builds on (most cited first, 17 of 17)

- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [On Fast Leverage Score Sampling and Optimal Learning](https://mlsanity.com/paper/1810.13258/) (2018)
- [Non-parametric Models for Non-negative Functions](https://mlsanity.com/paper/2007.03926/) (2020)
- [Learning the Parameters of Determinantal Point Process Kernels](https://mlsanity.com/paper/1402.4862/) (2014)
- [Finding Global Minima via Kernel Approximations](https://mlsanity.com/paper/2012.11978/) (2020)
- [Kernel interpolation with continuous volume sampling](https://mlsanity.com/paper/2002.09677/) (2020)
- [Bayesian experimental design using regularized determinantal point processes](https://mlsanity.com/paper/1906.04133/) (2019)
- [Learning Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/1905.12962/) (2019)
- [Fixed-point algorithms for learning determinantal point processes](https://mlsanity.com/paper/1508.00792/) (2015)
- [Low-Rank Factorization of Determinantal Point Processes for Recommendation](https://mlsanity.com/paper/1602.05436/) (2016)
- [Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/2006.09862/) (2020)
- [A determinantal point process for column subset selection](https://mlsanity.com/paper/1812.09771/) (2018)
- [Learning Determinantal Point Processes in Sublinear Time](https://mlsanity.com/paper/1610.05925/) (2016)
- [Adaptive estimating function inference for non-stationary determinantal point processes](https://mlsanity.com/paper/1806.06231/) (2018)
- [Gain with no Pain: Efficient Kernel-PCA by Nystr"om Sampling](https://mlsanity.com/paper/1907.05226/) (2019)
- [Wasserstein Learning of Determinantal Point Processes](https://mlsanity.com/paper/2011.09712/) (2020)
- [Inference for determinantal point processes without spectral knowledge](https://mlsanity.com/paper/1507.01154/) (2015)

## Abstract (arXiv)

Determinantal Point Process (DPPs) are statistical models for repulsive point patterns. Both sampling and inference are tractable for DPPs, a rare feature among models with negative dependence that explains their popularity in machine learning and spatial statistics. Parametric and nonparametric inference methods have been proposed in the finite case, i.e. when the point patterns live in a finite ground set. In the continuous case, only parametric methods have been investigated, while nonparametric maximum likelihood for DPPs -- an optimization problem over trace-class operators -- has remained an open question. In this paper, we show that a restricted version of this maximum likelihood (MLE) problem falls within the scope of a recent representer theorem for nonnegative functions in an RKHS. This leads to a finite-dimensional problem, with strong statistical ties to the original MLE. Moreover, we propose, analyze, and demonstrate a fixed point algorithm to solve this finite-dimensional problem. Finally, we also provide a controlled estimate of the correlation kernel of the DPP, thus providing more interpretability.