Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions

Key points

• Scaling DPP learning to large datasets typically requires imposing structural constraints on the kernel matrix, such as a low-rank-plus-diagonal form.1
• However, structural assumptions introduce a severe trade-off between expressive power and computational scalability.1
• 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.1
• Numerical experiments on real-world datasets demonstrate that our method significantly improves this trade-off, achieving better generalization performance with remarkable parameter efficiency.1

Sources (1)

• [1]Scalable Learning of Determinantal Point Processes with Kernel-Structured Interactions
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 9, 12:25 AM

  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.

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