Browsing by Author "Botha, Dylon"

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    Discriminant analysis using sparse graphical models
    (Stellenbosch : Stellenbosch University, 2020-03) Botha, Dylon; Kamper, Francois; Bierman, Surette; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY : The objective of this thesis is the proposal of a new classification method. This classification method is an extension of classical quadratic discriminant analysis (QDA), where the focus is placed on relaxing the assumption of normality, and on overcoming the adverse effect of the large number of parameters that needs to be estimated when applying QDA. To relax the assumption of normality, we consider assigning to each class density a different nonparanormal distribution. Based on these nonparanormal distributions, new discriminant functions can be derived. When one considers the use of a nonparanormal distribution, the underlying assumption is that the associated random vector, can through the use of an appropriate transformation, be made to follow a Gaussian distribution. Such a transformation is based on the marginals of the distribution, which is to be estimated in a nonparametric way. The large number of parameters in QDA is a result of the estimation of class precision matrices. To overcome this problem, penalised maximum likelihood estimation is performed by placing an L1 penalty on the size of the elements in the class precision matrices. This leads to sparse precision matrix estimates, and therefore also to a reduction in the number of estimated parameters. Combining the above approaches to overcome the problems induced by nonnormality and a large number of parameters to estimate, leads to the following novel classification method. To each class density, a separate transformation is applied. Thereafter L1 penalised maximum likelihood estimation is performed in the transformed space. The resulting parameter estimates are then plugged into the nonparanormal discriminant functions, thereby facilitating classification. An empirical evaluation of the novel proposal shows it to be competitive with a wide array of existing classifiers. We also establish a connection to probabilistic graphical models, which could aid in the interpretation of this new technique.