Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels
Abstract
Determinantal point processes (DPPs) model subset selection probability with repulsion, but many applications also exhibit attraction arising from pairwise relations or shared latent structures. Nonsymmetric DPPs (NDPPs) capture both effects, but their kernels are difficult to interpret and specify. 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. This formulation preserves the feature-based interpretation of standard DPPs while allowing the two effects to be specified separately. 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. 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. Conversely, nontransitive pair-specific attraction may require compensation through the DRPP repulsion kernel. Experiments support these predictions, showing that DRPPs fit transitive attraction with substantially fewer parameters than NDPPs.
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BibTeX
@misc{ishibashi2026generalized,
title = {{Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels}},
author = {Hideaki Ishibashi and Takahiro Kawashima and Hideitsu Hino},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12894},
eprint = {2610.12894},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12894},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels
AU - Hideaki Ishibashi
AU - Takahiro Kawashima
AU - Hideitsu Hino
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.12894
UR - https://arxiv.org/abs/2610.12894
AB - Determinantal point processes (DPPs) model subset selection probability with repulsion, but many applications also exhibit attraction arising from pairwise relations or shared latent structures. Nonsymmetric DPPs (NDPPs) capture both effects, but their kernels are difficult to interpret and specify. 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. This formulation preserves the feature-based interpretation of standard DPPs while allowing the two effects to be specified separately. 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. 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. Conversely, nontransitive pair-specific attraction may require compensation through the DRPP repulsion kernel. Experiments support these predictions, showing that DRPPs fit transitive attraction with substantially fewer parameters than NDPPs.
ER -