Efficient tensor operations and the method of moments

Joe Kileel, University of Texas, Austin
Fine Hall 214

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.