# Learning Nonsymmetric Determinantal Point Processes

arXiv: https://arxiv.org/abs/1905.12962 · HTML: https://mlsanity.com/paper/1905.12962/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 16 of 16)

- [Probabilistic Generating Circuits](https://mlsanity.com/paper/2102.09768/) (2021)
- [Fast parallel sampling under isoperimetry](https://mlsanity.com/paper/2401.09016/) (2024)
- [Determinantal Point Process Likelihoods for Sequential Recommendation](https://mlsanity.com/paper/2204.11562/) (2022)
- [From Sampling to Optimization on Discrete Domains with Applications to Determinant Maximization](https://mlsanity.com/paper/2102.05347/) (2021)
- [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)
- [WLD-Reg: A Data-dependent Within-layer Diversity Regularizer](https://mlsanity.com/paper/2301.01352/) (2023)
- [Small coresets via negative dependence: DPPs, linear statistics, and concentration](https://mlsanity.com/paper/2411.00611/) (2024)
- [Online MAP Inference and Learning for Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/2111.14674/) (2021)
- [Scalable Sampling for Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/2201.08417/) (2022)
- [Nonparametric estimation of continuous DPPs with kernel methods](https://mlsanity.com/paper/2106.14210/) (2021)
- [Computational Complexity of Normalizing Constants for the Product of Determinantal Point Processes](https://mlsanity.com/paper/2111.14148/) (2021)
- [Bypassing orthogonalization in the quantum DPP sampler](https://mlsanity.com/paper/2503.05906/) (2025)
- [A simple estimator of the correlation kernel matrix of a determinantal point process](https://mlsanity.com/paper/2505.14529/) (2025)
- [A Spectral Phase Admissibility Certificate for Complex Linear Maps](https://mlsanity.com/paper/2609.02911/) (2026)
- [Identication and Estimation of Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/2610.14520/) (2026)

## Abstract (arXiv)

Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive semi-definite kernel matrix, and this symmetric kernel encodes only repulsive interactions between items. These so-called symmetric DPPs have significant expressive power, and have been successfully applied to a variety of machine learning tasks, including recommendation systems, information retrieval, and automatic summarization, among many others. Efficient algorithms for learning symmetric DPPs and sampling from these models have been reasonably well studied. However, relatively little attention has been given to nonsymmetric DPPs, which relax the symmetric constraint on the kernel. Nonsymmetric DPPs allow for both repulsive and attractive item interactions, which can significantly improve modeling power, resulting in a model that may better fit for some applications. We present a method that enables a tractable algorithm, based on maximum likelihood estimation, for learning nonsymmetric DPPs from data composed of observed subsets. Our method imposes a particular decomposition of the nonsymmetric kernel that enables such tractable learning algorithms, which we analyze both theoretically and experimentally. We evaluate our model on synthetic and real-world datasets, demonstrating improved predictive performance compared to symmetric DPPs, which have previously shown strong performance on modeling tasks associated with these datasets.