Markov Properties of Discrete Determinantal Point Processes

Kayvan Sadeghi, Alessandro Rinaldo
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:1313-1321, 2019.

Abstract

Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and direct way. Discrete DPPs have become popular and computationally tractable models for solving several machine learning tasks that require the selection of diverse objects, and have been successfully applied in numerous real-life problems. Despite their popularity, the statistical properties of such models have not been adequately explored. In this note, we derive the Markov properties of discrete DPPs and show how they can be expressed using graphical models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-sadeghi19a, title = {Markov Properties of Discrete Determinantal Point Processes}, author = {Sadeghi, Kayvan and Rinaldo, Alessandro}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {1313--1321}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/sadeghi19a/sadeghi19a.pdf}, url = {https://proceedings.mlr.press/v89/sadeghi19a.html}, abstract = {Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and direct way. Discrete DPPs have become popular and computationally tractable models for solving several machine learning tasks that require the selection of diverse objects, and have been successfully applied in numerous real-life problems. Despite their popularity, the statistical properties of such models have not been adequately explored. In this note, we derive the Markov properties of discrete DPPs and show how they can be expressed using graphical models.} }
Endnote
%0 Conference Paper %T Markov Properties of Discrete Determinantal Point Processes %A Kayvan Sadeghi %A Alessandro Rinaldo %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-sadeghi19a %I PMLR %P 1313--1321 %U https://proceedings.mlr.press/v89/sadeghi19a.html %V 89 %X Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and direct way. Discrete DPPs have become popular and computationally tractable models for solving several machine learning tasks that require the selection of diverse objects, and have been successfully applied in numerous real-life problems. Despite their popularity, the statistical properties of such models have not been adequately explored. In this note, we derive the Markov properties of discrete DPPs and show how they can be expressed using graphical models.
APA
Sadeghi, K. & Rinaldo, A.. (2019). Markov Properties of Discrete Determinantal Point Processes. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:1313-1321 Available from https://proceedings.mlr.press/v89/sadeghi19a.html.

Related Material