PhD Thesis Defense: "Dealing with Dimensionality: Problems and Techniques in High-Dimensional Statistics"

Abstract: In modern data analysis, high dimensional data with more variables than subjects is increasingly common. Two such cases where this phenomenon arises is during mediation analysis and in distributed optimization. In chapter 2 we start with an overview of high dimensional statistics and mediation analysis to motivate the considered problems. In chapter 3 we motivate and prove properties for a new marginal screening procedure for performing high dimensional mediation analysis. This screening procedure is shown via simulation to perform better than benchmark approaches and is applied to a DNA methylation study. In chapter 4 we motivate and construct a cryptosystem that accurately performs distributed penalized quantile regression in the high-dimensional setting using a divide-and-conquer approach while preserving the privacy of subject data.

Host: Nan Lin