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In computational mathematics a tensor is an array of numbers.Ìý It can have more than two indices, and thus generalizes a matrix.Ìý Operations with higher-order tensors, e.g. low-rank decompositions, enjoy stronger uniqueness properties than matrix factorizations in linear algebra do.Ìý However, often they are intractable in theory (due to being NP-hard) and also practice (due to their high dimensionality).Ìý In this talk, I’ll present a simple idea that addresses some of these challenges for tensors arising as moments of multivariate datasets.Ìý 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.ÌýÌý Time permitting, I’ll mention a new bound for tensor completion, and show a simulation involving image denoising.Ìý

The talk is based on joint work with João Pereira, Tamara Kolda and Yifan Zhang. ÌýÌý