ABSTRACT
This chapter discusses the problem of edge estimation in undirected graphical models, also known as Markov networks. Given observations from a joint distribution, the goal is to construct an estimate of the edge set of the underlying graph. The chapter presents algorithms for edge estimation for multivariate Gaussian and Ising models, focusing on population-level results and then discussing statistical theory. It considers generally fall into one of two categories, either involving estimating the adjacency matrix of the graph based on the support of an appropriate matrix, or estimating individual node neighborhoods via penalized regression. The chapter describes generalizations of the methods to other classes of distributions, as well as adaptations for contaminated or incomplete data. It explores several practical algorithms for edge recovery in Gaussian graphical models. The chapter suggests that adaptations of the neighborhood selection techniques that allow for consistent estimation of the edge set, even in the presence of contamination.
