Geomstats: Riemannian geometry, statistics, and programming

Geomstats is an open-source Python package for computations, and statistics on nonlinear manifolds. We provide object-oriented and extensively unit-tested implementations. Manifolds can be equipped with Riemannian metrics with associated exponential and logarithmic maps, geodesics, and parallel transport. Some manifolds can also be endowed with additional mathematical structures, such as Lie group, or fiber bundle structures. Statistics and learning algorithms provide methods for estimation, clustering, and dimensionality reduction on manifolds. All associated operations are supported in different backends, namely NumPy, Autograd, and PyTorch. In this talk, we briefly introduce the main concepts in Riemannian geometry and discuss the package design. We show that Geomstats provides reliable building blocks to both foster research in differential geometry and statistics and democratize the use of Riemannian geometry in statistics and machine learning. The source code is freely available under the MIT license at https://github.com/geomstats/geomstats. Contatti: paola.antonietti@polimi.it edie.miglio@polimi.it marco.verani@polimi.it