# Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions

arXiv: https://arxiv.org/abs/2610.12829 · HTML: https://mlsanity.com/paper/2610.12829/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 43 references that are in the map.
- First posted on arXiv 9 Oct 2026.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement](https://mlsanity.com/paper/1903.06059/) (2019)
- [D4: Improving LLM Pretraining via Document De-Duplication and Diversification](https://mlsanity.com/paper/2308.12284/) (2023)
- [No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis](https://mlsanity.com/paper/1704.00708/) (2017)
- [On the Diversity of Synthetic Data and its Impact on Training Large Language Models](https://mlsanity.com/paper/2410.15226/) (2024)
- [Learning the Parameters of Determinantal Point Process Kernels](https://mlsanity.com/paper/1402.4862/) (2014)
- [Expectation-Maximization for Learning Determinantal Point Processes](https://mlsanity.com/paper/1411.1088/) (2014)
- [Active Mini-Batch Sampling using Repulsive Point Processes](https://mlsanity.com/paper/1804.02772/) (2018)
- [Deterministic guarantees for Burer-Monteiro factorizations of smooth semidefinite programs](https://mlsanity.com/paper/1804.02008/) (2018)
- [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)
- [Learning Determinantal Point Processes in Sublinear Time](https://mlsanity.com/paper/1610.05925/) (2016)
- [Revisiting Random Binning Features: Fast Convergence and Strong Parallelizability](https://mlsanity.com/paper/1809.05247/) (2018)
- [Hardness of Maximum Likelihood Learning of DPPs](https://mlsanity.com/paper/2205.12377/) (2022)
- [MS-DPPs: Multi-Source Determinantal Point Processes for Contextual Diversity Refinement of Composite Attributes in Text to Image Retrieval](https://mlsanity.com/paper/2507.06654/) (2025)
- [From DPPs to k-DPPs: identifiability analysis via spectral decomposition](https://mlsanity.com/paper/2605.25526/) (2026)
- [Deep Determinantal Point Processes](https://mlsanity.com/paper/1811.07245/) (2018)

## Abstract (arXiv)

Determinantal point processes (DPPs) on a finite set are probability models that exhibit repulsion where inter-item similarities are encoded by a positive definite kernel matrix. Scaling DPP learning to large datasets typically requires imposing structural constraints on the kernel matrix, such as a low-rank-plus-diagonal form. However, structural assumptions introduce a severe trade-off between expressive power and computational scalability. Our study addresses this challenge by (a) modeling the full-rank interactions via a nonlinear kernel function and latent features, (b) designing a surrogate function for the maximum likelihood estimator, and (c) adopting stochastic optimization using random features of the nonlinear kernel. Numerical experiments on real-world datasets demonstrate that our method significantly improves this trade-off, achieving better generalization performance with remarkable parameter efficiency.