Testing Determinantal Point Processes

Determinantal point processes (DPPs) are popular probabilistic models of diversity. In this paper, we investigate DPPs from a new perspective: property testing of distributions. Given sample access to an unknown distribution q over the subsets of a ground set, we aim to distinguish whether q is a DPP distribution, or (sic)-far from all DPP distributions in '1-distance. In this work, we propose the first algorithm for testing DPPs. Furthermore, we establish a matching lower bound on the sample complexity of DPP testing, up to logarithmic factors. This lower bound also implies a new hardness result for the problem of testing the more general class of log-submodular distributions.