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Learning determinantal point processes

Presented by: 
Philippe Rigollet Massachusetts Institute of Technology
Friday 19th January 2018 - 09:45 to 10:30
INI Seminar Room 1
Co-authors: Victor-Emmanuel Brunel (MIT), Ankur Moitra (MIT), John Urschel (MIT)

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 (such as recommendation systems) 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. In this talk, I will present recent results related to this problem, specifically - Rates of convergence for the maximum likelihood estimator: by studying the local and global geometry of the expected log-likelihood function we are able to establish rates of convergence for the MLE and give a complete characterization of the cases where these are parametric. We also give a partial description of the critical points for the expected log-likelihood. - Optimal rates of convergence for this problem: these are achievable by the method of moments and are governed by a combinatorial parameter, which we call the cycle sparsity. - A fast combinatorial algorithm to implement the method of moments efficiently.

The necessary background on DPPs will be given in the talk.

Joint work with Victor-Emmanuel Brunel (M.I.T), Ankur Moitra (M.I.T) and John Urschel (M.I.T).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons