Events for 02/13/2024 from all calendars

Fast Tensor Methods and Implicit Computations

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Joao Pereira

Description: In this talk I will focus on fast methods for analysing and decomposing tensor data. In the first part of the talk, I will introduce a method we proposed for symmetric tensor decomposition. We provide several guarantees for the algorithm and its relevant non-convex optimization problem. Furthermore, we observe empirically that the method is roughly one order of magnitude faster than existing decomposition algorithms, and is also robust to noise. On the second part of the talk, I will cover implicit method of moments. Higher-order moments of multivariate random variables suffer from a curse of dimensionality: the number of entries scale exponentially with the order of the moments. We introduce an implicit approach that allows for estimating parameters without explicitly forming the moments, that way avoiding the curse of dimensionality. We use this approach to estimate the parameters of Gaussian Mixture Models, obtaining a method with computational and storage costs similar to those of state-of-the arts methods, such as expectation-maximization, and opening the door to the practical use of the method of moments for multivariate variables. Finally, I will mention several related methods and applications, including on-going work on using the method introduced in the first part of the talk for decomposing moment tensors implicitly.