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Title: Total positivity in structured binary distributions Authors:  Piotr Zwiernik - Universitat Pompeu Fabra (Spain) [presenting]
Caroline Uhler - Massachusetts Institute of Technology (United States)
Steffen Lauritzen - University of Copenhagen (Denmark)
Abstract: Binary distributions are studied which are multivariate totally positive of order 2 (MTP2). Binary distributions can be represented as an exponential family and we show that MTP2 exponential families are convex. Moreover, MTP2 quadratic exponential families, which contain ferromagnetic Ising models and attractive Gaussian graphical models, are defined by intersecting the space of canonical parameters with a polyhedral cone whose faces correspond to conditional independence relations. Hence MTP2 serves as an implicit regularizer for quadratic exponential families and leads to sparsity in the estimated graphical model. The analysis of data from two psychological disorders will be provided.