Estimation of Graphical Models: An Overview of Selected Topics

• Published in: International statistical review Vol. 92; no. 2; pp. 194 - 245
• Main Author: Chen, Li‐Pang
• Format: Journal Article
• Language: English
• Published: Hoboken John Wiley & Sons, Inc 01-08-2024
• Subjects: Algorithms; Bayesian analysis; Classification; complex and noisy data; Complex variables; computational algorithm; conditional inference; Data structures; graphical LASSO; graphical models; Machine learning; multivariate linear models; network structure; Nonparametric statistics; optimisation; pairwise dependence; Statistical inference; Supervised learning
• ISSN: 0306-7734; 1751-5823
• DOI: 10.1111/insr.12552

Summary
Graphical modelling is an important branch of statistics that has been successfully applied in biology, social science, causal inference and so on. Graphical models illuminate connections between many variables and can even describe complex data structures or noisy data. Graphical models have been combined with supervised learning techniques such as regression modelling and classification analysis with multi‐class responses. This paper first reviews some fundamental graphical modelling concepts, focusing on estimation methods and computational algorithms. Several advanced topics are then considered, delving into complex graphical structures and noisy data. Applications in regression and classification are considered throughout.