City Research Online

Abstract

This thesis explores the use of convex optimisations to address two types of problems. In the first chapter, we review the nearest correlation matrix problem, a problem in actuarial science and finance, to find the nearest correlation matrix that is positive semidefinite. We introduce two algorithms to solve the problem, namely the iterative quadratic/linear programming method and the gradient descent method. The iterative quadratic/linear programming method enjoys great flexibility so that it can handle different types of norms and user-defined constraints. The gradient descent method works for unconstrained problems under the Frobenius norm and experiments show that it is resilient to noise. In the second chapter, we explore the fair learning problem. We introduce different definitions of fairness in classification tasks and how they can be generalised into regressions. We propose two fair regression models based on Liu-type estimator, using the expected squared difference of the pairwise linear components and coefficient of determination of the sensitive features as measures of fairness, respectively. The first method works with a single sensitive feature while the second method can include multidimensional sensitive features into its model. Both models can be calculated as closed form solutions. In the third chapter, we continue our study of the fair learning problem and propose a fair generalised linear model framework that uses the maximum mean discrepancy as the fairness measure. Our choice of fairness measure can capture more complex differences between distributions from different sensitive groups. The model can be applied to datasets with different outcome types so is suitable for both classification and regression tasks.

Publication Type:	Thesis (Doctoral)
Subjects:	H Social Sciences > HA Statistics
Departments:	Bayes Business School > Actuarial Science & Insurance Bayes Business School > Bayes Business School Doctoral Theses Doctoral Theses

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