UC Davis

Statistical machine learning methods are widely used in various fields such as astrophysics, biomedical research, genetics, education, and recruitment. While much attention has been directed toward point estimation, several critical facets, including interval estimation, hypothesis testing, and algorithmic discrimination (where models perform differently for different groups), remain relatively under explored. This dissertation includes three projects that address complex data analysis tasks across fields of selection bias correction, spatial point segmentation, and high-dimensional mediation analysis, and contributes to the problem of algorithmic fairness and uncertainty quantification in their respective domains. Chapter 2 addresses the fairness of regression problems, aiming at mitigating the disparity between two demographic groups. Our proposed method adaptsto distribution shifts induced by selection bias through a weighting technique. Chapter 3 and Chapter 4 concentrate on refining methods for segmenting irregular regions of extended astronomical emission and quantifying associated uncertainty by constructing global confidence regions of a two-dimensional boundary. Lastly, Chapter 5 studies high-dimensional mediation analysis within biomedical research, proposing new techniques to fill methodological gaps and developing inference tools to identify mediators from observational data.