Romain Couillet

Featured Articles

A Random Matrix Approach to Neural Networks. [article] This article introduces a new approach to analyze the performance of large dimensional neural networks by means of random matrix theory. In this first step towards a deeper understanding of involved neural networks, we consider a single layer extreme learning machine and prove the convergence of its performance as the dataset and number of neurons grow simultanesouly large. The landmark technical result is to alleviate the non-linearity of the induced random matrix model by the exploitation of new concentration of measure arguments.

Kernel Spectral Clustering of Large Dimensional Data. [article] This article provides a first analysis of kernel spectral clustering methods for a mixture of Gaussian data inputs. It is shown here that, for large dimensional datasets, the spectral clustering performance relates to the properties of the isolated eigenvectors in a spiked random matrix models. Through toy examples, we provide in particular a better understanding of the role of the kernel function. Applications to real (non Gaussian) datasets also illustrate a strong proximity between theory and practice.

Spectral community detection in heterogeneous large networks. [preprint] This article proposes a new community detection algorithm for realistic heterogeneous graphs based on the degree-corrected stochastic block model. The proposed algorithm generalizes several classical spectral methods by the addition of a parameter that can be optimally selected from the degrees of the graph, and is proved to be asymptotically optimal among this class of estimators.

The Random Matrix Regime of Maronna's M-estimator with elliptically distributed samples. [article] In this article, we provide a first bridge between the theories of robust estimation and random matrices. We show in particular that the eigenvalue distribution of a family of M-estimators of population covariance matrices has the same first order behavior as a classical random matrix model. This entails important results such as the natural extension of random matrix-based detection and estimation methods, e.g. spectrum-based source detection and power inference, the G-MUSIC algorithm for DoA estimation, etc.





Book Chapters



HDR Thesis

R. Couillet, "Robust Estimation Methods in the Large Random Matrix Regime", CentraleSupélec, February 2015. [thesis|slides]
Composition of the jury:

PhD Thesis

R. Couillet, "Application of random matrix theory to future wireless flexible networks", Supélec, November 2010. [thesis|slides]
Composition of the jury: