# A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence

arXiv: https://arxiv.org/abs/2408.01022 · HTML: https://mlsanity.com/paper/2408.01022/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 61 references that are in the map.
- First posted on arXiv 2 Aug 2024.

## Builds on (most cited first, 17 of 17)

- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks](https://mlsanity.com/paper/1301.3853/) (2013)
- [A Langevin-like Sampler for Discrete Distributions](https://mlsanity.com/paper/2206.09914/) (2022)
- [Determinantal Point Processes in Randomized Numerical Linear Algebra](https://mlsanity.com/paper/2005.03185/) (2020)
- [Expectation-Maximization for Learning Determinantal Point Processes](https://mlsanity.com/paper/1411.1088/) (2014)
- [Bayesian experimental design using regularized determinantal point processes](https://mlsanity.com/paper/1906.04133/) (2019)
- [Fixed-point algorithms for learning determinantal point processes](https://mlsanity.com/paper/1508.00792/) (2015)
- [Low-Rank Factorization of Determinantal Point Processes for Recommendation](https://mlsanity.com/paper/1602.05436/) (2016)
- [Precise expressions for random projections: Low-rank approximation and randomized Newton](https://mlsanity.com/paper/2006.10653/) (2020)
- [Provable Submodular Minimization using Wolfe's Algorithm](https://mlsanity.com/paper/1411.0095/) (2014)
- [Learning Determinantal Point Processes in Sublinear Time](https://mlsanity.com/paper/1610.05925/) (2016)
- [Fast Semidifferential-based Submodular Function Optimization](https://mlsanity.com/paper/1308.1006/) (2013)
- [Kronecker Determinantal Point Processes](https://mlsanity.com/paper/1605.08374/) (2016)
- [Lost Relatives of the Gumbel Trick](https://mlsanity.com/paper/1706.04161/) (2017)
- [Unbiased estimators for random design regression](https://mlsanity.com/paper/1907.03411/) (2019)
- [Gradient-Guided Importance Sampling for Learning Binary Energy-Based Models](https://mlsanity.com/paper/2210.05782/) (2022)
- [Fast Mixing for Discrete Point Processes](https://mlsanity.com/paper/1506.02194/) (2015)

## Built on by (most cited first, 2 of 2)

- [Adaptive Quality-Diversity Trade-offs for Large-Scale Batch Recommendation](https://mlsanity.com/paper/2602.02024/) (2026)
- [Generalized Determinantal Point Processes for Attraction and Repulsion with Distinct Interaction Kernels](https://mlsanity.com/paper/2610.12894/) (2026)

## Abstract (arXiv)

Positive and negative dependence are fundamental concepts that characterize the attractive and repulsive behavior of random subsets. Although some probabilistic models are known to exhibit positive or negative dependence, it is challenging to seamlessly bridge them with a practicable probabilistic model. In this study, we introduce a new family of distributions, named the discrete kernel point process (DKPP), which includes determinantal point processes and parts of Boltzmann machines. We also develop some computational methods for probabilistic operations and inference with DKPPs, such as calculating marginal and conditional probabilities and learning the parameters. Our numerical experiments demonstrate the controllability of positive and negative dependence and the effectiveness of the computational methods for DKPPs.