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Activity Number: 636 - Graphical Models: From Foundations to Applications
Type: Invited
Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #300371 Presentation
Title: Total Positivity and Graphical Models
Author(s): Piotr Zwiernik and Caroline Uhler*
Companies: Universitat Pompeu Fabra and Massachusetts Institute of Technology
Keywords: multivariate total positivity; graphical models; M-matrices; sparse structures

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. The main aim of this talk is to given an idea of what the MTP2 condition is as well as to show how total positivity becomes useful in graphical modelling.

Authors who are presenting talks have a * after their name.

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