Parameter Learning for Log-supermodular Distributions

Tatiana Shpakova 1, 2 Francis Bach 1, 2
1 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : We consider log-supermodular models on binary variables, which are probabilistic models with negative log-densities which are submodular. These models provide probabilistic interpretations of common combinatorial optimization tasks such as image segmentation. In this paper, we focus primarily on parameter estimation in the models from known upper-bounds on the intractable log-partition function. We show that the bound based on separable optimization on the base polytope of the submodular function is always inferior to a bound based on " perturb-and-MAP " ideas. Then, to learn parameters, given that our approximation of the log-partition function is an expectation (over our own randomization), we use a stochastic subgradient technique to maximize a lower-bound on the log-likelihood. This can also be extended to conditional maximum likelihood. We illustrate our new results in a set of experiments in binary image denoising, where we highlight the flexibility of a probabilistic model to learn with missing data.
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Communication dans un congrès
NIPS 2016 - Thirtieth Annual Conference on Neural Information Processing System, Dec 2016, Barcelona, Spain
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Tatiana Shpakova, Francis Bach. Parameter Learning for Log-supermodular Distributions. NIPS 2016 - Thirtieth Annual Conference on Neural Information Processing System, Dec 2016, Barcelona, Spain. 〈hal-01354789v2〉

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