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Niklas Koep

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2 papers

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JMLR Journal 2020 Journal Article

Geomstats: A Python Package for Riemannian Geometry in Machine Learning

Nina Miolane
Nicolas Guigui
Alice Le Brigant
Johan Mathe
Benjamin Hou
Yann Thanwerdas
Stefan Heyder
Olivier Peltre

We introduce Geomstats, an open-source Python package 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. 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. This paper presents the package, compares it with related libraries, and provides relevant code examples. 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 machine learning applications. The source code is freely available under the MIT license at geomstats.ai. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2020. ( edit, beta )

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JMLR Journal 2016 Journal Article

Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation

James Townsend
Niklas Koep
Sebastian Weichwald

Optimization on manifolds is a class of methods for optimization of an objective function, subject to constraints which are smooth, in the sense that the set of points which satisfy the constraints admits the structure of a differentiable manifold. While many optimization problems are of the described form, technicalities of differential geometry and the laborious calculation of derivatives pose a significant barrier for experimenting with these methods. We introduce Pymanopt (available at pymanopt.github.io ), a toolbox for optimization on manifolds, implemented in Python, that---similarly to the Manopt Matlab toolbox---implements several manifold geometries and optimization algorithms. Moreover, we lower the barriers to users further by using automated differentiation for calculating derivative information, saving users time and saving them from potential calculation and implementation errors. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

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