Description du sujet de thèse

The past few years have witnessed major breakthroughs in the field of Artificial Intelligence (AI).
Computers can now understand human language, transcribe texts, recognise patterns and even drive
cars. The backbone of these developments is Machine Learning, the field dealing with how machines
learn from data. Despite the impressive technological advances, the theoretical understanding of
modern machine learning models falls short. The traditional statistical analysis developed in the early
20th century struggle to deal with the modern regime in which the number of model parameters
are of the same order as the quantity of data - a problem known as the the curse of dimensionality
(CoD). Understanding why the algorithms employed in the day-a-day practice of Machine Learning
work so well despite the CoD is therefore a major theoretical challenge, and is paramount for a wider
acceptance of these methods in sensitive applications, such as medicine and healthcare.
This project is concerned with one key aspect in this problem: the role played by structure in data
in the success of Machine Learning algorithms.

The candidate will study structure in its different forms, from sparsity to generative models, in the context of simple models that are mathematically tractable. For that, he/she will employ a combination of both classical tools, such as high-dimensional probability and random matrix theory, with tools from the statistical physics of disordered systems literature. By the end of the thesis, we hope to have a better understanding of the interplay between feature and structure learning in machine learning.

Contexte de travail

The candidate will join the Centre for Data Science at the École Normale Supérieure in Paris, a multi-disciplinary initiative grouping researchers from the department of Computer Science, Mathematics, Cognitive Sciences and Physics of ENS.