Algorithms for regression and classification

Abstract

Regression and classification are statistical techniques that may be used to extract rules and patterns out of data sets. Analyzing the involved algorithms comprises interdisciplinary research that offers interesting problems for statisticians and computer scientists alike. The focus of this thesis is on robust regression and classification in genetic association studies.

In the context of robust regression, new exact algorithms and results for robust online scale estimation with the estimators Qn and Sn and for robust linear regression in the plane with the estimator least quartile difference (LQD) are presented. Additionally, an evolutionary computation algorithm for robust regression with different estimators in higher dimensions is devised. These estimators include the widely used least median of squares (LMS) and least trimmed squares (LTS).

For classification in genetic association studies, this thesis describes a Genetic Programming algorithm that outpeforms the standard approaches on the considered data sets. It is able to identify interesting genetic factors not found before in a data set on sporadic breast cancer and to handle larger data sets than the compared methods. In addition, it is extendible to further application fields.