Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions

Takahiro Kawashima; Hideitsu Hino

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arXiv · 2610.12829

Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions

Takahiro Kawashima·Hideitsu Hino

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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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Takahiro Kawashima, Hideitsu Hino. 2026-10-09. Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions. https://arxiv.org/abs/2610.12829

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