PACM Colloquium, Prof. Joseph Kileel, UT Austin

Efficient tensor operations and the method of moments

Abstract: In computational mathematics a tensor is an array of numbers.  It can have more than two indices, and thus generalizes a matrix.  Operations with higher-order tensors, e.g. low-rank decompositions, enjoy stronger uniqueness properties than matrix factorizations in linear algebra do.  However, often they are intractable in theory (due to being NP-hard) and also practice (due to their high dimensionality). 

In this talk, I’ll present a simple idea that addresses some of these challenges for tensors arising as moments of multivariate datasets.  I'll describe tensor-based methods for fitting mixture models to data applying to Gaussian mixtures and a class of other models, which are competitive with – and arguably more flexible than – leading non-tensor-based approaches.   Time permitting, I’ll mention a new bound for tensor completion, and show a simulation involving image denoising.  The talk is based on joint work with João Pereira, Tamara Kolda and Yifan Zhang.   

Bio: Joseph Kileel is an assistant professor in the Department of Mathematics and Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin since 2020.  From 2017-2020 he was a postdoc at the Program in Applied and Computational Mathematics at Princeton University.  He obtained the PhD in mathematics from the University of California, Berkeley in 2017.  Joe's research relates broadly to applied mathematics and computational algebra.