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

Graphical structure of conditional independencies in determinantal point processes