Both from a theoretical and a methodological viewpoints, low-rank tensor estimation from noisy data is a difficult problem, yet 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 random tensors, opening a new window into their spectral properties and allowing one to reach several predictions that had been previously obtained only with the statistical physics machinery.
Seminar H. Goulart: A random matrix perspective on random tensor models
Monday, February 15, 2021 - 14:00 to 15:15
Online (Zoom) / L'Atrium (RdC, bâtiment ESPRIT) for a live broadcast
CNRS, INP ENSEEIHT, Institut de Recherche en Informatique de Toulouse (IRIT)