Estimation of Graphical Models: An Overview of Selected Topics

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.