1 p.m. - 2 p.m. Location: FN 2.102
School of Statistics
University of Minnesota
Geometric Statistics for High-Dimensional Data Analysis
We present a scheme of studying the geometry of high-dimensional data to discover patterns in it, using minimal parametric distributional assumptions. Our approach is to define multivariate quantiles and extremes, and develop a method of center-outward partial ordering of observations. We formulate methods for quantifying relationships among observed variables, thus generalizing the notions of regression and principal components. We propose tests for linear relations between variables in many dimensions using the geometric properties of the data, thus paving a way for checking whether recent developments involving Gaussian assumption or sparsity of relations are applicable. We devise geometric algorithms for detection of outliers in high dimensions, classification and supervised learning. Examples on the use the proposed methods will be provided. This is joint work with several students.
Coffee to be served in FN 2.102 30 minutes prior to the talk.