Graphical structure of conditional independencies in determinantal point processes
This work addresses a theoretical problem for researchers using determinantal point processes, but it appears incremental as it builds on existing characterizations without introducing a new paradigm.
The paper tackles the problem of characterizing conditional independence in determinantal point processes, a model used in machine learning, by describing some conditional independencies through kernel conditions and showing many can be derived from the graph induced by the kernel.
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.