University of Texas at Austin

Past Event: Babuška Forum

Tensor decomposition in data science

Joe Kileel, Assistant Professor, Oden Institute, Department of Math, UT Austin

10 – 11AM
Friday Nov 6, 2020

Zoom Meeting - Babuška Forum series

Abstract

Tensors are higher-order matrices, and decomposing tensors can reveal structure in datasets. In recent years, tensor decomposition has found applications in statistics, computational imaging, signal processing, and quantum chemistry. In this talk, we will present a new numerical method for low-rank symmetric tensor decomposition, building on the usual power method and ideas from classical algebraic geometry. The approach achieves a speed-up over the state-of-the-art by roughly one order of magnitude. We will also describe an “implicit” variant of the algorithm for the case of moment tensors which avoids the explicit formation of higher-order moments, analogously to matrix-free techniques in linear algebra. Time permitting, we will mention various open problems in the subject, concerning numerical stability, non-convex optimization, random behavior and challenging applications. This is based on joint works with Joao Pereira, Tammy Kolda and Timo Klock. Bio Joe Kileel is an Assistant Professor of the Oden Institute and Mathematics Department at UT Austin, since August 2020. Prior to this, he was a Simons postdoctoral fellow at the Program in Applied and Computational Mathematics, Princeton University and he obtained a PhD in Mathematics from UC Berkeley in 2017. His research interests are in mathematics of data, computational algebra, tensor methods, inverse problems and non-convex optimization. (The Babuška Forum series was started by Professor Ivo Babuška several years ago to expose students to interesting and curious topics relevant to computational engineering and science with technical content at the graduate student level (i.e. the focus of the lectures is on main ideas with some technical content). Seminar credit is given to those students who attend.)
Tensor decomposition in data science

Event information

Date
10 – 11AM
Friday Nov 6, 2020
Location Zoom Meeting - Babuška Forum series
Hosted by Stefan Henneking