ABSTRACT
This chapter aims to assuming Gaussianity leads to a rich geometric structure that can be exploited for parameter estimation. It discusses maximum likelihood (ML) estimation for Gaussian graphical models. There are two problems of interest in this regard: to estimate the edge weights that is the canonical parameters, given the graph structure, and to learn the underlying graph structure. The chapter shows that ML estimation for Gaussian graphical models is a convex optimization problem and describes its dual optimization problem. It analyzes this dual optimization problem and explains the close links to positive definite matrix completion problems studied in linear algebra. The chapter provides a geometric picture of ML estimation for Gaussian graphical models that complements the point of view of convex optimization. It deals with a discussion of other Gaussian models with linear constraints on the concentration matrix or the covariance matrix.
