Structure Learning in Graphical Modeling

TL;DR

This paper reviews recent advances in structure learning for graphical models, focusing on methods for estimating underlying graph structures in multivariate data, including techniques for both directed and undirected models.

Contribution

It provides a comprehensive overview of recent methods and extensions for structure learning in graphical models, highlighting advances like graphical lasso, neighborhood selection, and algorithms for latent variables.

Findings

Discusses the effectiveness of graphical lasso and neighborhood selection.

Reviews algorithms like PC and score-based search for directed models.

Highlights extensions for latent variables and heterogeneous data.

Abstract

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit computationally convenient factorization properties and have long been a valuable tool for tractable modeling of multivariate distributions. More recently, applications such as reconstructing gene regulatory networks from gene expression data have driven major advances in structure learning, that is, estimating the graph underlying a model. We review some of these advances and discuss methods such as the graphical lasso and neighborhood selection for undirected graphical models (or Markov random fields), and the PC algorithm and score-based search methods for directed graphical models (or Bayesian networks). We further review extensions that account for effects of latent variables and heterogeneous data sources.