Infosheet (January 9th, 2018)

Queen's University - Department of Mathematics and Statistics

Wednesday, January 10

Special Colloquium

Time: 3:30 p.m.

Place: Jeffery 234

Speaker: Zhenhua Lin, University of Toronto

Title: Intrinsic Riemannian Functional Data Analysis

Abstract Attached

Friday, January 12

Department Colloquium

Time: 2:30 p.m.

Place: Jeffery 234

Speaker: Yifan Cui, University of North Carolina at Chapel Hill

Title: Tree-based Survival Models and Precision Medicine

Abstract Attached

Items for the Info Sheet should reach Anne ( by noon on Monday. The Info Sheet is published every Tuesday.

Wednesday, January 10, 3:30 p.m. Jeffery 234 Special Colloquium

Speaker: Zhenhua Lin

Title: Intrinsic Riemannian Functional Data Analysis

Abstract: Data of random paths on a Riemannian manifold is often encountered in real-world applications. Examples include trajectories of bird migration, the dynamics of brain functional connectivity, etc. To analyze such data, a framework of intrinsic Riemannian functional data analysis is developed, which provides a rigorous theoretical foundation for statistical analysis of random paths on a Riemannian manifold. The cornerstone of the framework is the Hilbert space of vector fields along a curve on the manifold, based on which principal component analysis and Karhunen-Loève expansion for Riemannian random paths are then established. The framework also features a proposal for proper comparison of vector fields along different curves, which paves the way for intrinsic asymptotic analysis of estimation procedures for Riemannian functional data analysis. Built on intrinsic geometric concepts such as vector field, Levi-Civita connection and parallel transport on Riemannian manifolds, the proposed framework embraces full generality of applications and proper handle of intrinsic geometric concepts. Based on the framework, functional linear regression models for Riemannian random paths are investigated, including estimation methods, asymptotic properties and an application to the study of brain functional connectivity.

Friday, January 12, 2:30 p.m. Jeffery 234 Department Colloquium

Speaker: Yifan Cui

Title: Tree-based Survival Models and Precision Medicine

Abstract: In the first part, we develop a theoretical framework for survival tree and forest models. We first investigate the method from the aspect of splitting rules. We show that existing approaches lead to a potentially biased estimation of the within-node survival and cause non-optimal selection of the splitting rules. Based on this observation, we develop an adaptive concentration bound result which quantifies the variance component for survival forest models. Furthermore, we show with three specific examples how these concentration bounds, combined with properly designed splitting rules, yield consistency results. In the second part, we focus on one application of survival trees in precision medicine which estimates individualized treatment rules nonparametrically under right censoring. We extend the outcome weighted learning to right censored data without requiring either inverse probability of

censoring weighting or semi-parametric modeling of the censoring and failure times. To accomplish this, we take advantage of the tree-based approach to nonparametrically impute the survival time in two

different ways. In simulation studies, our estimators demonstrate improved performance compared to existing methods. We also illustrate the proposed method on a phase III clinical trial of non-small cell lung cancer.

Contact Info

Department of Math & Stats
Jeffery Hall, 48 University Ave.
Kingston, ON Canada, K7L 3N6
Phone: (613) 533-2390
Fax: (613) 533-2964
Office Hours: 8:30am-12:00pm & 1:00pm-4:30pm