4:00 pm Monday, December 5, 2022
Colloquium: Efficient tensor operations and the method of moments by Joe Kileel (UT) in PMA 5.104
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 in practice (due to their high dimensionality). In this talk, I’ll present an idea that addresses some of these challenges for tensors arising as moments of multivariate datasets. I will describe new tensor-based methods for fitting mixture models to data applying to Gaussian mixtures and a class of other mixtures, which in some cases perform better with the leading non-tensor-based estimation approaches. Different applications will be discussed, as well as a new bound for filling in missing entries of a low-rank tensor. Based on joint work with João Pereira, Tamara Kolda and Yifan Zhang. Submitted by
|
|