Markov Properties of Discrete Determinantal Point Processes
This work addresses a gap in the theoretical understanding of DPPs, which are widely applied in machine learning for tasks requiring diversity, but it is incremental as it focuses on foundational statistical properties rather than new applications or major breakthroughs.
The authors tackled the problem of understanding the statistical properties of discrete determinantal point processes (DPPs), which are used for modeling diverse object selection in machine learning, by deriving their Markov properties and expressing them using graphical models.
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.