Learning Determinantal Point Processes with Moments and Cycles


John Urschel, Victor-Emmanuel Brunel, Ankur Moitra, Philippe Rigollet ;
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3511-3520, 2017.


Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important. While there are fast algorithms for sampling, marginalization and conditioning, much less is known about learning the parameters of a DPP. Our contribution is twofold: (i) we establish the optimal sample complexity achievable in this problem and show that it is governed by a natural parameter, which we call the cycle sparsity; (ii) we propose a provably fast combinatorial algorithm that implements the method of moments efficiently and achieves optimal sample complexity. Finally, we give experimental results that confirm our theoretical findings.

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