Date of Award

8-1-2023

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Dissertation/Thesis Chair

Yunlong Feng

Committee Members

Yunlong Feng, Yiming Ying, Alex Valm, Penghang Yin

Keywords

Biological Spectral Imaging, Robust Statistical Learning

Subject Categories

Physical Sciences and Mathematics

Abstract

This thesis investigates robust statistical learning and its applications in biological spectral imaging. The first part of this thesis addresses the challenges raised in the statistical learning of robust expectile regression. Expectiles can be obtained through empirical risk minimization (\acrshort{erm}), which minimizes the sum of asymmetrically weighted squared deviations. However, this \acrshort{erm} scheme lacks robustness to abnormal observations and flexibility. To overcome these limitations, we adopt the empirical gain maximization (\acrshort{egm}) scheme that learns expectiles using an asymmetric Gaussian \acrshort{egm} approach. The corresponding \acrshort{erm} can be formulated with a robust expectile loss, which is bounded and nonconvex. Through a learning theory analysis, we explore the relationship between the asymmetric Gaussian \acrshort{egm} approach and the expectile regression model. Our findings demonstrate that the expectile level and the scale parameter in the loss function trade off the convergence rates and robustness of the regression model.

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