Graphical models under total positivity

Title: Graphical models under total positivity

Abstract: We discuss properties of distributions that are multivariate totally positive of order two (MTP2). Such distributions appear in the context of positive dependence, ferromagnetism in the Ising model, and various latent models. While such distributions have a long history in probability theory and statistical physics, in this talk I will discuss such distributions in the context of high dimensional statistics and graphical models. In particular, I will show that MTP2 in the Gaussian setting implies sparsity and existence of the MLE already for 2 observations independent of the number of variables, making this an interesting alternative to the graphical lasso for various applications.