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Type
Abstract
A method for extracting multiscale geometric features from a data cloud is presented. Each pair of data points is mapped into a real-valued feature function, whose construction is based on geometric considerations and the novel notion of a distribution of (local) data depths. The collection of these feature functions is then being used for further data analysis. In contrast to the popular kernel-trick, our feature functions are functions of a one-dimensional parameter, and thus they can be used to visualize geometric aspects of a high-dimensional data cloud. Besides visualization, applications include classification and anomaly detection. The performance of the methodology is illustrated through applications to real data sets, and some theoretical guarantees supporting the performance of the proposed methodology are presented. This is joint work with G. Chandler.
Bio
Prof. Polonik’s research interests include Mathematical Statistics, Nonparametric Statistics, Shape Constraints, Modality, Nonstationary Time Series, Empirical Process Theory, Topological Data Analysis, Random Networks. He was associate editors for several journals JRSS-B (2012-2015), Annals of Statistics (2007-2012), Journal of Multivariate Analysis (since 2003) and Journal of Statistical Planning and Interference (2004-2012). Find more of him on his website: http://www.stat.ucdavis.edu/~polonik/WP-personal-home.html
Prof. Polonik’s research interests include Mathematical Statistics, Nonparametric Statistics, Shape Constraints, Modality, Nonstationary Time Series, Empirical Process Theory, Topological Data Analysis, Random Networks. He was associate editors for several journals JRSS-B (2012-2015), Annals of Statistics (2007-2012), Journal of Multivariate Analysis (since 2003) and Journal of Statistical Planning and Interference (2004-2012). Find more of him on his website: http://www.stat.ucdavis.edu/~polonik/WP-personal-home.html
Description
Statistics Seminar
Friday, December 3
2:00pm MST/AZ
Virtual via Zoom
https://asu.zoom.us/j/88521538236?pwd=K1VscVlWTmFnN0tsRHlrWG8rT0Nhdz09
Meeting ID: 885 2153 8236
Password: ASUSTATS
Speaker
Wolfgang Polonik
Professor
Department of Statistics
UC Davis
Location
Virtual via Zoom