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Thu Dec 10 08:30 AM -- 08:40 AM (PST) @ Orals & Spotlights: Probabilistic Models/Statistics
Testing Determinantal Point Processes
Khashayar Gatmiry · Maryam Aliakbarpour · Stefanie Jegelka
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 $\epsilon$-far from all DPP distributions in $\ell_1$-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. This lower bound also extends to showing a new hardness result for the problem of testing the more general class of log-submodular distributions.