Chair objectives

Tensor-based methods enjoy great success and popularity in machine learning, playing a prominent role in modern artificial intelligence (AI), and more generally in the analysis of data arising in numerous scientific domains such as signal processing and chemometrics.

And yet, the actual performance of these methods and of the approximate tensor decomposition algorithms which lie at their heart are, to a large extent, not well understood.

Moreover, existing performance guarantees oftentimes rely on conditions which are too stringent or whose validity in practice is hard to assess, especially in the common modern regime where the number of observations and their dimension are of comparable size.


Such a state of affairs is at odds with the current needs for devising provably reliable AI systems and for precisely characterizing their limitations.

This chair aims at bridging these gaps, by carrying out a precise quantification of the performance of tensor-based machine learning methods, and more generally of tensor decomposition algorithms, in the largedimensional regime where the observed data have high dimension, which is commonplace in contemporary applications.

To achieve this goal, it will build upon and extend an approach recently introduced by the PI for the study of large random tensor models by relying on tools from random matrix theory and highdimensional statistics.

This research program shall lead to new results on fundamental questions related to the properties and the estimation of random tensor models. In particular, the performance limits of tensorbased methods and tensor decomposition algorithms will be investigated.

We will then capitalize on the obtained results in order to develop improved and provably reliable tensor-based machine learning methods and tensor decomposition algorithms for large-dimensional data.

L’équipe de la chaire est composée de deux chercheurs aux compétences complémentaires, ce qui permet d’obtenir une combinaison d’outils qui permettra d’apporter des contributions majeures au sujet susmentionné.  Le porteur de la chaire est un expert en méthodes tensorielles et en l’analyse des modèles de tenseurs aléatoires, tandis que le co-chair est un expert des statistiques en haute dimension et en application de la théorie des matrices aléatoires pour l’analyse des algorithmes de ML.

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