Graph-theoretic methods in discrimination and classification

Thesis

This thesis is concerned with the graphical modelling of multivariate data. The main aim of graphical modelling is to provide an easy to understand visual representation of, often complex, data relationships by fitting graphs to data. The graphs consist of nodes denoting random variables and connecting lines or edges are used to depict variable dependencies. Equivalently, the absence of particular edges in a graph describe conditional independencies between random variables. The resulting structure is called a conditional independence graph.

The use of conditional independence graphs as a guide to discrete (mainly binary), normal and mixed conditional Gaussian model building is described. The problem of parameter estimation in fitting conditional Gaussian models is considered. A FORTRAN 77 program called CGM is developed and used to fit conditional Gaussian models. Submodel specification, model selection criteria and goodness-of-fit are explored.

A procedure for discriminating between groups is constructed using fitted conditional Gaussian models. A Bayesian classification procedure is considered and is used to compute posterior classification probabilities. Standard bias-correcting error rates are used to test the performance of estimated classification rules.

The graph-theoretic methodology described in this thesis is applied to a Scandinavian study of intrauterine foetal growth retardation also known as a small-for-gestational age (SGA) birth. Possible pre-pregnancy risk factors associated with SGA births are investigated using conditional independence graphs and an attempt is made to classify SGA births using fitted conditional Gaussian models.

Authors: Saldanha, R

• Peer review status: Peer reviewed
• DOI: 10.5287/ora-pmy6j9905
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford