# Low-Rank Factorization of Determinantal Point Processes for Recommendation

arXiv: https://arxiv.org/abs/1602.05436 · HTML: https://mlsanity.com/paper/1602.05436/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2016.

## Built on by (most cited first, 14 of 14)

- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [PURS: Personalized Unexpected Recommender System for Improving User Satisfaction](https://mlsanity.com/paper/2106.02771/) (2021)
- [Determinantal Point Process Likelihoods for Sequential Recommendation](https://mlsanity.com/paper/2204.11562/) (2022)
- [Feasible Recourse Plan via Diverse Interpolation](https://mlsanity.com/paper/2302.11213/) (2023)
- [Hardness of Maximum Likelihood Learning of DPPs](https://mlsanity.com/paper/2205.12377/) (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)
- [LDDR: Linear-DPP-Based Dynamic-Resolution Frame Sampling for Video MLLMs](https://mlsanity.com/paper/2605.11477/) (2026)
- [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)
- [Efficient Failure Pattern Identification of Predictive Algorithms](https://mlsanity.com/paper/2306.00760/) (2023)
- [A simple estimator of the correlation kernel matrix of a determinantal point process](https://mlsanity.com/paper/2505.14529/) (2025)
- [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)

Determinantal point processes (DPPs) have garnered attention as an elegant probabilistic model of set diversity. They are useful for a number of subset selection tasks, including product recommendation. DPPs are parametrized by a positive semi-definite kernel matrix. In this work we present a new method for learning the DPP kernel from observed data using a low-rank factorization of this kernel. We show that this low-rank factorization enables a learning algorithm that is nearly an order of magnitude faster than previous approaches, while also providing for a method for computing product recommendation predictions that is far faster (up to 20x faster or more for large item catalogs) than previous techniques that involve a full-rank DPP kernel. Furthermore, we show that our method provides equivalent or sometimes better predictive performance than prior full-rank DPP approaches, and better performance than several other competing recommendation methods in many cases. We conduct an extensive experimental evaluation using several real-world datasets in the domain of product recommendation to demonstrate the utility of our method, along with its limitations.