Seminar in Random Tensors

Date: February 19, 2021

Time: 11:00AM - 12:00PM

Location: zoom

Speaker: Henrique Goulart, U. Toulouse

Title: A random matrix perspective on spiked tensor models

Abstract: Both from a theoretical and a methodological viewpoints, low-rank tensor estimation from noisy data is a difficult problem, however rich of a host of applications in numerous domains. Though many different methods have been developed to address it, no theory is available for predicting their performance in practice. Progress has been recently made by studying the asymptotic performance of estimators of certain so-called spiked tensor models, the dimensions of which are assumed to be rather large. Yet, these results rely upon techniques and concepts borrowed from statistical physics, which are largely inaccessible to non-experts and difficult to extend to other, more general tensor models. In this talk, I will show how standard but powerful tools from random matrix theory can be leveraged to study these low-rank tensor estimators, opening a new window into spectral properties of random tensors and allowing one to reach several predictions that had been previously obtained only with the statistical physics machinery.