Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions
Abstract
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.
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BibTeX
@misc{kawashima2026scalable,
title = {{Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions}},
author = {Takahiro Kawashima and Hideitsu Hino},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12829},
eprint = {2610.12829},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12829},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions
AU - Takahiro Kawashima
AU - Hideitsu Hino
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.12829
UR - https://arxiv.org/abs/2610.12829
AB - 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.
ER -