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B1352
Title: Sparsity in Gaussian totally positive distributions Authors:  Piotr Zwiernik - University of Toronto (Canada) [presenting]
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, which provides an interesting alternative to the graphical lasso method.