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IDSS Special Seminar

Graphical models under total positivity

September 27, 2018 @ 4:00 pm - 5:00 pm

Caroline Uhler (MIT)


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.

MIT Statistics + Data Science Center
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139-4307