# Learning Determinantal Point Processes in Sublinear Time

arXiv: https://arxiv.org/abs/1610.05925 · HTML: https://mlsanity.com/paper/1610.05925/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2016.

## Built on by (most cited first, 8 of 8)

- [Hardness of Maximum Likelihood Learning of DPPs](https://mlsanity.com/paper/2205.12377/) (2022)
- [Scalable MCMC Sampling for Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/2207.00486/) (2022)
- [Scalable Sampling for Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/2201.08417/) (2022)
- [A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence](https://mlsanity.com/paper/2408.01022/) (2024)
- [Nonparametric estimation of continuous DPPs with kernel methods](https://mlsanity.com/paper/2106.14210/) (2021)
- [Duality induced by an embedding structure of determinantal point process](https://mlsanity.com/paper/2404.11024/) (2024)
- [Adaptive Quality-Diversity Trade-offs for Large-Scale Batch Recommendation](https://mlsanity.com/paper/2602.02024/) (2026)
- [Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions](https://mlsanity.com/paper/2610.12829/) (2026)

## Abstract (arXiv)

We propose a new class of determinantal point processes (DPPs) which can be manipulated for inference and parameter learning in potentially sublinear time in the number of items. This class, based on a specific low-rank factorization of the marginal kernel, is particularly suited to a subclass of continuous DPPs and DPPs defined on exponentially many items. We apply this new class to modelling text documents as sampling a DPP of sentences, and propose a conditional maximum likelihood formulation to model topic proportions, which is made possible with no approximation for our class of DPPs. We present an application to document summarization with a DPP on 2500 items.