aiqbench analysis
This research introduces the Determinant-Ratio Point Process (DRPP), a novel mathematical framework that decouples attraction and repulsion effects in subset selection models using distinct interaction kernels. By enabling efficient sampling and tractable learning, this method offers significant parameter efficiency improvements over existing nonsymmetric DPPs for modeling complex latent structures like clustered groups. The work advances the theoretical toolkit for machine learning applications requiring precise control over both positive and negative correlations within data subsets.
Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels
arXiv:2610.12894v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG); Computation (stat.CO)
arXiv:2610.12894 [stat.ML]
(or arXiv:2610.12894v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.12894 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 282 words
Related coverage
Distributional Determinantal Point Process for Repulsive Clustering of Distributions
arXiv · Jul 27, 2026
Salesforce after Dreamforce: How the CRM giant can grow beyond its own interface
SiliconANGLE · Sep 19, 2026
Lattice-Based Cryptography Explained
Quantum Zeitgeist · Aug 15, 2026
LiveLaw Supreme Court Half-Yearly Digest: January - June 2026 [Part 2]
livelaw.in · Sep 13, 2026