Eindhoven Stochastic Seminar
Jan 26, 15:45 - 16:45
Modelling with positive dependence: graphical models, and convex optimization
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. Although very useful in some applications, the MTP2 may result in a too restrictive model for some positively dependent data. The main aim of this lecture is to present a particularly tractable relaxation of the MTP2 property. I will also briefly introduce the GOLAZO algorithm which offers a flexible approach for learning sparsity in Gaussian distributions that takes into account positive dependence.
This talk is based on joint work with Steffen Lauritzen.