Graphical structure of conditional independencies in determinantal point processes

Tvrtko Tadić

Published 2014-06-21, updated 2014-06-29Version 2

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.