Since the work of E. Wigner in the fifties of the last century, large random matrices have been studied intensively in various branches of Mathematics and Physics such as high dimensional probability and statistics, operator algebras, number theory, particles physics, quantum chaos among others.
These matrices were introduced at the end of the nineties in electrical engineering in the field of digital communications. Their use in statistical signal processing is even more recent (2005). The goal of this summer school is to show how some fundamental statistical signal processing techniques and machine learning algorithms can be better understood and revisited in situations in which a (large) M dimensional multivariate time series is observed on a temporal window N of the same order of magnitude than M.
The accent will be put on array processing, robust estimation, and community detection on graphs using tools from large random matrix theory.
This summer school is organized in the framework of the French Agence Nationale de la Recherche (ANR) projects DIONISOS (program “modèles numériques”) and RMT4GRAPHS. The partners are CentraleSupélec, Institut Eurecom, Telecom ParisTech and Université Paris-Est Marne-la-Vallée.
Some useful references :
- Pascal Vallet, Xavier Mestre, Philippe Loubaton, “Performance analysis of an improved MUSIC DoA estimator“, IEEE Trans. on Signal Processing, vol. 63, no. 23, pp. 6407-6422, December 1 2015, also available on Arxiv (arXiv:1503.01271)
- H. Tiomoko Ali, R. Couillet, “Performance analysis of spectral community detection in realistic graph models”, IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’16), Shangai, China, 2016
- R. Couillet, F. Benaych-Georges, “Kernel Spectral Clustering of Large Dimensional Data“, (submitted to) Electronic Journal of Statistics, 2015.