arXiv Machine Learning By Hideaki Ishibashi, Takahiro Kawashima, Hideitsu Hino

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

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The paper introduces the determinant-ratio point process (DRPP), a new model that captures both attraction and repulsion in subset selection by using a ratio of determinants from two symmetric positive-definite kernels. DRPP retains the feature-based interpretability of standard determinantal point processes while allowing separate specification of attraction and repulsion effects. The authors provide an auxiliary-variable representation that enables efficient MCMC sampling and tractable expectation formulas, facilitating maximum-likelihood learning, and theoretically show that DRPP can realize clustered attraction with fewer parameters than nonsymmetric DPPs.

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