EE SEminar: Optimal thresholding of singular values and eigenvalues
(The talk will be given in English)
Speaker: Prof. Matan Gavish
School of Computer Science and Engineering, Hebrew University
Wednesday, March 15th, 2017
15:00 - 16:00
Room 011, Kitot Bldg., Faculty of Engineering
Optimal thresholding of singular values and eigenvalues
Abstract
It is common practice in multivariate and matrix-valued data analysis to reduce dimensionality by performing a Singular Value Decomposition or Principal Component Analysis, and keeping only r singular values or principal components, the rest being presumably associated with noise. However, the literature does not propose a disciplined criterion to determine r; most practitioners still look for the ``elbow in the Scree Plot'', a 50-years-old heuristic performed by eye. I'll review a line of work which develops a systematic approach to eigenvalue and singular value thresholding. This approach assumes that the signal is low-rank and that the noise is rotationally invariant. Recent results derive optimal thresholds in the presence of quite general noise distributions.
Joint work with David Donoho, Iain Johnstone and Edgar Dobriban (Stanford).
Bio
Matan is an assistant professor at the Hebrew University of Jerusalem School of Computer Science and Engineering. He received the dual B.Sc. degree in Mathematics and Physics from Tel Aviv University (TAU) in 2006, the M.Sc. degree in Mathematics from the Hebrew University of Jerusalem in 2008 (supervised by Hillel Furstenberg) and the Ph.D. degree in Statistics from Stanford University in 2014 (supervised by David Donoho and Ronald Coifman). His research interests include applied harmonic analysis, high-dimensional statistics, computing and machine learning. He was in the Adi Lautman Interdisciplinary Program for outstanding students at TAU from 2002 to 2006 and held a William R. and Sara Hart Kimball Stanford Graduate Fellowship from 2009 to 2012.
