no code implementations • 10 May 2024 • Florent Bouchard, Ammar Mian, Malik Tiomoko, Guillaume Ginolhac, Frédéric Pascal
In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fr\'echet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means.
no code implementations • 8 Nov 2023 • Florent Bouchard, Alexandre Renaux, Guillaume Ginolhac, Arnaud Breloy
In this setup, the chosen Riemannian metric induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure.
no code implementations • 2 Oct 2023 • Florent Bouchard, Arnaud Breloy, Antoine Collas, Alexandre Renaux, Guillaume Ginolhac
When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric.
1 code implementation • 21 Oct 2022 • Alexandre Hippert-Ferrer, Florent Bouchard, Ammar Mian, Titouan Vayer, Arnaud Breloy
Graphical models and factor analysis are well-established tools in multivariate statistics.
no code implementations • 19 Oct 2021 • Alexandre Hippert-Ferrer, Ammar Mian, Florent Bouchard, Frédéric Pascal
This paper proposes a strategy to handle missing data for the classification of electroencephalograms using covariance matrices.
no code implementations • 20 May 2020 • Florent Bouchard, Ammar Mian, Jialun Zhou, Salem Said, Guillaume Ginolhac, Yannick Berthoumieu
A new Riemannian geometry for the Compound Gaussian distribution is proposed.
no code implementations • 7 Feb 2019 • Malik Tiomoko, Florent Bouchard, Guillaume Ginholac, Romain Couillet
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics.