Graphical structure of conditional independencies in determinantal point processes

TL;DR

This paper explores the graphical structure of conditional independencies in determinantal point processes, providing kernel-based characterizations and insights into their graphical representations.

Contribution

It introduces new kernel-based conditions for conditional independence and connects these to the graph structure induced by the $L$-ensemble in determinantal point processes.

Findings

Conditional independencies can be characterized through kernel conditions.

Graphical representations of DPPs can be derived from the $L$-ensemble.

Many conditional independencies are obtainable via the induced graph.

Abstract

Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional independence. We describe some conditional independencies through the conditions on the kernel of a determinantal point process, and show many can be obtained using the graph induced by a kernel of the $L$-ensemble.