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

arXiv: https://arxiv.org/abs/2610.12894 · HTML: https://mlsanity.com/paper/2610.12894/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Batch Active Learning Using Determinantal Point Processes](https://mlsanity.com/paper/1906.07975/) (2019)
- [Probabilistic Generating Circuits](https://mlsanity.com/paper/2102.09768/) (2021)
- [Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications](https://mlsanity.com/paper/1408.2051/) (2014)
- [Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/2006.09862/) (2020)
- [Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD](https://mlsanity.com/paper/2112.06007/) (2021)
- [From Sampling to Optimization on Discrete Domains with Applications to Determinant Maximization](https://mlsanity.com/paper/2102.05347/) (2021)
- [Scalable MCMC Sampling for Nonsymmetric Determinantal Point Processes](https://mlsanity.com/paper/2207.00486/) (2022)
- [A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence](https://mlsanity.com/paper/2408.01022/) (2024)
- [The Bayesian Low-Rank Determinantal Point Process Mixture Model](https://mlsanity.com/paper/1608.04245/) (2016)

## Abstract (arXiv)

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.