Speaker
Description
Low-rank decompositions of moment tensors provide a natural approach for density and parameter estimation of mixture models, given data samples. In general, the mixture condition corresponds to the structure of a convex linear combination in terms of moment tensors. Therefore, moments of mixture models have low-rank tensor decompositions. Furthermore, computing the low-rank factors often reveals the parameters of interest quite directly.
All of this is rather well known in theory. But thus far, it has had a muted impact on practice, primarily because computations with high-order and high-dimensional tensors seem prohibitively expensive.
In this talk, I will describe work I have been doing that breaks down this barrier. The main theme will be the development of numerical algorithms for moment tensor decompositions that evade the apparent curse of dimensionality inherent in moment tensors. I will discuss results for a range of mixture models, including Gaussian mixture models, mixtures of products, and mixtures of nonparametric distributions with banded correlations. Time permitting, some real-life scientific applications will be mentioned, to highlight the practical improvements brought by the new methods.