MIOLANE, Nina; GUIGUI, Nicolas; LE BRIGANT, Alice; MATHE, Johan; HOU, Benjamin; THANWERDAS, Yann; HEYDER, Stefan; PELTRE, Olivier; KOEP, Niklas; ZAATITI, Hadi; HAJRI, Hatem; CABANES, Yann; GERALD, Thomas; CHAUCHAT, Paul; SHEWMAKE, Christian; BROOKS, Daniel; KAINZ, Bernhard; DONNAT, Claire; HOLMES, Susan; PENNEC, Xavier

Métadonnées

Licence d’utilisation du document

MIOLANE, Nina
Department of Statistics [Stanford]

GUIGUI, Nicolas
Université Côte d'Azur [UniCA]
E-Patient : Images, données & mOdèles pour la médeciNe numériquE [EPIONE]

LE BRIGANT, Alice
Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) [SAMM]

Langue

Article de revue

Ce document a été publié dans

Journal of Machine Learning Research. 2020-12-20, vol. 21, n° 223, p. 1-9

Microtome Publishing

Résumé en anglais

We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-oriented and extensively unit-tested implementations. Among others, manifolds come equipped with families of Riemannian metrics, with associated exponential and logarithmic maps, geodesics and parallel transport. Statistics and learning algorithms provide methods for estimation, clustering and dimension reduction on manifolds. All associated operations are vectorized for batch computation and provide support for different execution backends, namely NumPy, PyTorch and TensorFlow, enabling GPU acceleration. This paper presents the package, compares it with related libraries and provides relevant code examples. We show that Geomstats provides reliable building blocks to foster research in differential geometry and statistics, and to democratize the use of Riemannian geometry in machine learning applications. The source code is freely available under the MIT license at http://geomstats.ai.< Réduire

Mots clés en anglais

differential geometry

Riemannian geometry

statistics

machine learning

manifold

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191694

Projet Européen

G-Statistics - Foundations of Geometric Statistics and Their Application in the Life Sciences

Project ANR

Idex UCA JEDI - ANR-15-IDEX-0001
3IA Côte d'Azur

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251