Moment Tensor Decompositions

Abstract: In this talk I will present applications and new methods for decomposing higher-order moment tensors into appropriate low-rank representations.  In particular, I will describe a simple approach to avoid the curse of dimensionality when computing with moment tensors, and apply this to the learning of Gaussian mixture models as well as certain nonparametric mixtures.  I will describe special algebraic structure that arises in the application of the method of moments to 3D reconstruction problems in imaging, and explain how to incorporate priors like sparsity into the framework.  Time permitting, some analysis of the nonconvex optimization landscapes that arise in tensor decompositions may be mentioned.

Speaker Bio: Joe Kileel is an assistant professor at UT Austin in the Department of Mathematics and Oden Institute for Computational Engineering and Sciences since 2020.  He completed his PhD at UC Berkeley in 2017, and was a postdoctoral fellow at Princeton University from 2017-2020.  Joe’s research interests include computational algebra, tensor methods, nonconvex optimization and 3D reconstruction in computer vision and structural biology.