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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2610.12829 [stat.ML]

(or arXiv:2610.12829v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.12829 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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