Estimation of large-dimensional tensor models and applications in machine learning

31/03/2021 – 01/04/2021 all-day

Offre en lien avec l’Action/le Réseau : – — –/– — –

Laboratoire/Entreprise : IRIT (SC team, located at ENSEEIHT site)
Durée : 5 to 6 months
Contact :
Date limite de publication : 2021-03-31

Contexte :
Tensor models are powerful tools for addressing many problems in signal processing, machine learning and beyond. Yet, their use in these applications typically requires estimating a low-rank tensor from a set of observations corrupted by noise, which is often a difficult task. Moreover, in most cases there is currently no theory for predicting the actual estimation performance that can be attained.

To overcome this gap, in recent years several researchers have studied the asymptotic statistical performance of ideal and practical estimators in the large-dimensional regime, where the size of the tensor grows large. In particular, these works have uncovered the abrupt phase transition that the performance of an ideal estimator may undergo as the signal-to-noise ratio grows. While some important advancements have been achieved, many scenarios of practical interest remain unexplored, as well as the practical implications of the existing results in applications.

Sujet :
The overall goal of this internship is to study extensions and applications of the existing results, as a first step for pushing the existing theory beyond its current limits. We will in particular consider extensions to more general tensor models that apply to larger classes of real-world problems, including e.g. asymmetric models. Application to practical machine learning problems — such as community detection in hypergraphs, latent variable model estimation and high-order co-clustering — will also be considered.

The intern will initially perform computer simulations aimed at understanding the behavior of ideal and practical estimators in the target scenarios/applications. Some theoretical results may then be derived on the basis of these experimental findings. Scientific dissemination of these findings will also be encouraged, via publication of papers and/or participation in scientific events.

A PhD thesis may be proposed to the intern at the end.

Please refer to the attached document for further details.

Profil du candidat :
We look for strongly motivated candidates with a solid background on mathematics and statistics, having good programming skills in scientific computing languages (Python, Matlab, Julia). Basic knowledge or interest in random matrix theory is a strong plus.

Formation et compétences requises :
Master 2 student in applied math, statistics, computer science, signal processing or other related fields.

Adresse d’emploi :
2, rue Charles Camichel
31071 Toulouse, France

Document attaché : 202010191312_M2-internship-2021.pdf