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Activity Number: 105
Type: Invited
Date/Time: Monday, August 1, 2016 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract #318255 View Presentation
Title: Totally Positive Exponential Families, Graphical Models, and Convex Optimization
Author(s): Piotr Zwiernik* and Caroline Uhler and Steffen Lauritzen
Companies: Pompeu Fabra University and MIT and University of Copenhagen
Keywords: total positivity ; graphical models ; quadratic exponential families ; convex optimization ; submodularity ; conditional independence
Abstract:

Probability distributions that are multivariate totally positive of order 2 (MTP2) appeared in the theory of positive dependence and in statistical physics through the celebrated FKG inequality. The MTP2 property is stable under marginalization, conditioning and it appears naturally in various probabilistic graphical models with hidden variables. Models of exponential families with the MTP2 property admit a unique maximum likelihood estimator. In the Gaussian case, the MLE exists also in high-dimensional settings, when p>>n, and it leads to sparse solutions. In many cases this may provide an alternative to the standard graphical lasso algorithm.


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