# Kronecker Determinantal Point Processes

arXiv: https://arxiv.org/abs/1605.08374 · HTML: https://mlsanity.com/paper/1605.08374/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2016.

## Built on by (most cited first, 6 of 6)

- [Probabilistic Generating Circuits](https://mlsanity.com/paper/2102.09768/) (2021)
- [Multiple-criteria Based Active Learning with Fixed-size Determinantal Point Processes](https://mlsanity.com/paper/2107.01622/) (2021)
- [Hardness of Maximum Likelihood Learning of DPPs](https://mlsanity.com/paper/2205.12377/) (2022)
- [A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence](https://mlsanity.com/paper/2408.01022/) (2024)
- [Duality induced by an embedding structure of determinantal point process](https://mlsanity.com/paper/2404.11024/) (2024)
- [Identication and Estimation of Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/2610.14520/) (2026)

## Abstract (arXiv)

Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of N items. They have recently gained prominence in several applications that rely on "diverse" subsets. However, their applicability to large problems is still limited due to the mathcal O(N3) complexity of core tasks such as sampling and learning. We enable efficient sampling and learning for DPPs by introducing KronDPP, a DPP model whose kernel matrix decomposes as a tensor product of multiple smaller kernel matrices. This decomposition immediately enables fast exact sampling. But contrary to what one may expect, leveraging the Kronecker product structure for speeding up DPP learning turns out to be more difficult. We overcome this challenge, and derive batch and stochastic optimization algorithms for efficiently learning the parameters of a KronDPP.