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FIELD
AI and Natural Sciences
DATE
Feb 21 (Tue), 2023
TIME
14:00 ~ 16:00
PLACE
7323
SPEAKER
Jung, Sungkyu
HOST
Lee, Jongmin
INSTITUTE
Department of Statistics, Seoul National University
TITLE
Statistics for objects that can not be averaged, with a case study on the space of eigen-decompositions
ABSTRACT
This talk consists of two parts. The first part is intended for a general audience, and we will discuss the role of average in statistics, and how the notion of the average generalizes for the case where objects are not easily averaged. The powerful notion of Frechet means and generalized Frechet means will be introduced. In the second part, we study extensions of Frechet means for random objects in the space of symmetric positive-definite matrices. The framework is designed to enjoy a clearer interpretation for the changes in random ellipsoids in terms of scaling and rotation. On a theoretical side, we discuss the existence and uniqueness of Frechet means, and a procedure of deriving strong consistency and a central limit theorem for M-estimators, defined in a non-metric and stratified space.
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