95 citations · 155 across the 23 of their papers we have counts for
11 papers · 1 filter
Riemannian statistics meets random matrix theory: towards learning from high-dimensional covariance matrices
Salem Said, Simon Heuveline, Cyrus Mostajeran
Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of…
Gaussian distributions on Riemannian symmetric spaces in the large N limit
Simon Heuveline, Salem Said, Cyrus Mostajeran
We consider Gaussian distributions on certain Riemannian symmetric spaces. In contrast to the Euclidean case, it is challenging to compute the normalization factors of such distrib…
Statistical models and probabilistic methods on Riemannian manifolds
Salem Said
This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis,…
Hidden Markov chains and fields with observations in Riemannian manifolds
Salem Said, Nicolas Le Bihan, Jonathan H. Manton
Hidden Markov chain, or Markov field, models, with observations in a Euclidean space, play a major role across signal and image processing. The present work provides a statistical…
The Riemannian barycentre as a proxy for global optimisation
Salem Said, Jonathan H. Manton
Let be a simply-connected compact Riemannian symmetric space, and a twice-differentiable function on , with unique global minimum at . The idea of the present…
Fast, asymptotically efficient, recursive estimation in a Riemannian manifold
Jialun Zhou, Salem Said
Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic opti…
Warped Riemannian metrics for location-scale models
Salem Said, Lionel Bombrun, Yannick Berthoumieu
The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in info…
Riemannian Gaussian distributions on the space of positive-definite quaternion matrices
Salem Said, Nicolas Le Bihan, Jonathan H. Manton
Recently, Riemannian Gaussian distributions were defined on spaces of positive-definite real and complex matrices. The present paper extends this definition to the space of positiv…
Warped metrics for location-scale models
Salem Said, Yannick Berthoumieu
This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports thr…
Gaussian distributions on Riemannian symmetric spaces: statistical learning with structured covariance matrices
Salem Said, Hatem Hajri, Lionel Bombrun +1
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data pro…
Riemannian Gaussian Distributions on the Space of Symmetric Positive Definite Matrices
Salem Said, Lionel Bombrun, Yannick Berthoumieu +1
Data which lie in the space , of symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications inclu…