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Learning and inference in probabilistic submodular models

Presented by: 
Andreas Krause
Tuesday 16th January 2018 - 11:45 to 12:30
INI Seminar Room 1
I will present our work on inference and learning in discrete probabilistic models defined through submodular functions. These generalize pairwise graphical models and determinantal point processes, express natural notions such as attractiveness and repulsion and allow to capture richly parameterized, long-range, high-order dependencies. The key idea is to use sub- and supergradients of submodular functions, and exploit their combinatorial structure to efficiently optimize variational upper and lower bounds on the partition function. This approach allows to perform efficient approximate inference in any probabilistic model that factorizes into log-submodular and log-supermodular potentials of arbitrary order. Our approximation is exact at the mode for log-supermodular distributions, and we provide bounds on the approximation quality of the log-partition function with respect to the curvature of the function. I will also discuss how to learn log-supermodular distributions via bi-level optimisation. In particular, we show how to compute gradients of the variational posterior, which allows integrating the models into modern deep architectures. This talk is primarily based on joint work with Josip Djolonga
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons