arXiv：cs.LG· Takahiro Kawashima, Hideitsu Hino·· 13 小时前
用核结构交互实现可扩展的行列式点过程学习
Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions
AI 导读
针对行列式点过程（DPP）学习中低秩加对角等结构约束带来的表达能力与计算可扩展性权衡，研究提出用非线性核函数与隐特征建模满秩交互，并设计最大似然估计的代理函数，采用非线性核随机特征的随机优化求解。在真实数据集上的数值实验显示，该方法显著改善这一权衡，以出色的参数效率取得更好的泛化性能。
正文
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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.12829 [stat.ML] |
| (or arXiv:2610.12829v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12829 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Takahiro Kawashima [view email]
[v1]
Fri, 9 Oct 2026 00:25:00 UTC (285 KB)
来源：arXiv：cs.LG · arxiv.org