Regression Model with Tree Structured Response
Yuan Wang, M.S. Candidate, Department of Statistics, Colorado State University
Tuesday, April 6, 2010
2:00 p.m., room 008, Statistics Bldg
Highly developed science and technology from last two decades motivated the study of complex data objects, which often lie in non-Euclidean spaces. In this paper, we considered tree-structured object, in particular its associated topological property. Our interest centers on modeling the relationship between tree-structured response variable and numerical covariates. Regression analysis has been a very powerful and widely-used toolkit for such purpose. For tree objects, this poses serious challenges since most regression methods relies on the linear operations in Euclidean space. We generalize the notion of local polynomial regression to the case of tree-structure response variable. In addition, a fast algorithm with theoretical justification is available. Our proposed method has been implemented to a data set of human's brain blood vessel trees.
Dr. Haonan Wang, Advisor
Dr. F. Jay Breidt, Committee Member
Dr. Jie Luo, Electrical & Computer Engineering, Outside Member