Graphical Models: Causal Inference and Total Positivity
Caroline Uhler, MIT

Graphical models are used throughout the natural and social sciences to model statistical relationships between variables of interest. In the first lecture, we will discuss directed graphical models for causal inference; in particular, how perturbation data such as gene knockout data can be used for causal structure discovery. In the second lecture, we will discuss undirected graphical models in the context of positive dependence. In applications ranging from finance to phylogenetics latent variables introduce positive dependence between variables. We will discuss how to model this using total positivity and the intriguing properties resulting from total positivity with respect to graphical models.