Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels

Key points

• We propose the determinant-ratio point process (DRPP), which models repulsion and attraction via a ratio of the determinants of two symmetric positive-definite kernels.1
• Furthermore, we introduce an auxiliary-variable representation that enables efficient MCMC sampling and yields tractable expectation formulas for key statistics including the normalizing constant, which together facilitate maximum-likelihood learning.1
• We theoretically characterize the interaction structures well suited to DRPPs: for clustered attraction with $C$ latent groups, DRPPs exactly realize the target pairwise interactions with an attraction rank $C$, whereas NDPPs can require a rank that grows with the number of items given the same repulsion component.1
• Conversely, nontransitive pair-specific attraction may require compensation through the DRPP repulsion kernel.1

Sources (1)

• [1]Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 9, 02:30 AM

  Determinantal point processes (DPPs) model subset selection probability with repulsion, but many applications also exhibit attraction arising from pairwise relations or shared latent structures.

  We propose the determinant-ratio point process (DRPP), which models repulsion and attraction via a ratio of the determinants of two symmetric positive-definite kernels.

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