High-dimensional statistics addresses settings in which the number of variables, the complexity of the objects, or the volume of data makes classical statistical methods inadequate. At L2S, these questions are studied by combining robust estimation, structured models, and optimization.

Our research aims to build reliable methods for data that may contain outliers, missing values, or only a small number of observations, and to exploit the geometry of covariance matrices and other non-Euclidean spaces. Applications include machine learning, radar, imaging, remote sensing, and biomedical data processing.

Research themes

Robust statistics in high dimensions

We study parameter estimation in the presence of outliers or contamination, in regimes where the dimension may be comparable to or larger than the number of observations. Our contributions include robust estimation of mean vectors and covariance or precision matrices, with statistically optimal or nearly minimax guarantees.

Covariance matrices and information geometry

Symmetric positive-definite matrices describe dependence between variables and are central objects in statistical signal processing. We develop methods based on random matrix theory, Fisher-Rao geometry, and Riemannian manifolds to improve their estimation, comparison, and averaging, especially when only a small number of samples is available.

Riemannian optimization and structured learning

Parameter structure can be incorporated directly into optimization algorithms through low-rank, sparsity, covariance, or graph constraints. Convex and Riemannian optimization therefore provide interpretable learning methods for multivariate data, including graph learning and factor models.