Ph.D. Defense: Meilei Jiang
Ph.D. Thesis Defense
Thursday, April 26th, 2018
324 Hanes Hall
Statistical Learning Of Integrative Analysis
(Under the direction of J. S. Marron and Jan Hannig)
Integrative analysis is of great interest in modern scientific research. This dissertation mainly focuses on developing new statistical methods for integrative analysis.
We first discuss a clustering analysis of a microbiome dataset in combination with phylogenetic information. Discovering disease related pneumotypes of the infected lower lung is difficult because the lower lung typically has few species of microbes and there is a low level of overlap from patient-to-patient, which makes it hard to calculate reliable distances between patients. We address this challenge by incorporating information from phylogenetic relationships, which results in improved clustering. When applied to an existing dataset, the method produces statistically distinct, easily described pneumotypes, which are better than those from standard approaches.
In the second part, we discuss an integrative analysis of disparate data blocks measured on a common set of experimental subjects. We introduce Angle-Based Joint and Individual Variation Explained (AJIVE) capturing both joint and individual variation within each data block. This is a major improvement over earlier approaches to this challenge in terms of a new conceptual understanding, much better adaption to data heterogeneity and a fast linear algebra computation. Detailed comparison between AJIVE and competitors is discussed using a particular optimization view point.
In the third part, we introduce a new perturbation framework, which estimates the angle between an arbitrary given direction and the underlying signal spaces. We also propose an efficient data-driven bootstrap procedure to compute this angle. While the Wedin bound in the AJIVE is “subspace oriented” and uniform for both row space and column space, this angle is “direction oriented” and specially adaptive to give improved inference in the row space.
*Please note that seating may be limited