Testing Determinantal Point Processes

• URL: http://arxiv.org/abs/2008.03650v1
• Date: Sun, 9 Aug 2020 04:45:16 GMT
• Title: Testing Determinantal Point Processes
• Authors: Khashayar Gatmiry (1), Maryam Aliakbarpour (1), Stefanie Jegelka (1) ((1) Massachusetts Institute of Technology)
• Abstract summary: We investigate DPPs from a new perspective: property testing of distributions. We propose the first algorithm for testing DPPs. We show a new hardness result for the problem of testing the more general class of log-submodular distributions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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