American Statistical Association
New York City
Metropolitan Area Chapter

Levin Lecture Series: Spring 2018 Colloquium Seminars
Department of Biostatistics
Columbia University



RECENT ADVANCES IN ELASTIC FUNCTIONAL DATA ANALYSIS

by

Anuj Srivastava
Distinguished Research Professor
Department of Statistics
Florida State University

Host: Dr. Todd Ogden


Abstract

Functional data analysis (FDA) is fast becoming an important research area, due to its broad applications in many branches of science, including biostatistics and bioinformatics. An essential component of FDA is registration of points across functional objects. Without proper registration, the results are often inferior and difficult to interpret. The current practice in FDA community is to treat registration as a pre-processing step, using off-the-shelf alignment procedures, and follow it up with statistical analysis of the resulting data. In contrast, Elastic FDA is a more comprehensive approach, where one solves for the registration and statistical inferences in a simultaneous fashion. The key idea here is to use Riemannian metrics with appropriate invariance properties, to form objective functions for alignment and to develop statistical models involving functional data. While these elastic metrics are complicated in general, we have developed a family of square-root transformations that map these metrics into simpler Euclidean representations, thus enabling more standard statistical procedures. Specifically, we have developed techniques for elastic functional PCA and elastic regression models involving functional variables. I will demonstrate this idea using imaging data in neuroscience and bioinformatics, where biological structures can often be represented as functions (curves or surfaces) on intervals or spheres. Examples of curves include DTI fiber tracts and chromosomes while examples of surfaces include subcortical structures (hippocampus, thalamus, putamen, etc.). Statistical goals here include shape analysis and modeling of these structures and to use their shapes in medical diagnosis.


Date: Thursday, May 3, 2018
Time: 11:30 A.M. - 12:30 P.M.
Location: Mailman School of Public Health
Department of Biostatistics
722 West 168th Street
AR Building
8th Floor Auditorium
New York, New York

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