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

Takahiro Kawashima, Hideitsu Hino
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:64-72, 2025.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-kawashima25a, title = {A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence}, author = {Kawashima, Takahiro and Hino, Hideitsu}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {64--72}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/kawashima25a/kawashima25a.pdf}, url = {https://proceedings.mlr.press/v258/kawashima25a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence %A Takahiro Kawashima %A Hideitsu Hino %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-kawashima25a %I PMLR %P 64--72 %U https://proceedings.mlr.press/v258/kawashima25a.html %V 258 %X 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.
APA
Kawashima, T. & Hino, H.. (2025). A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:64-72 Available from https://proceedings.mlr.press/v258/kawashima25a.html.

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