Abstract
We address here the construction of wrapped probability densities on Lie groups and quotient of Lie groups using the exponential map. The paper starts by briefly reviewing the different approaches to build densities on a manifold and shows the interest of wrapped distributions. We then construct wrapped densities on SE(n) and discuss their statistical estimation. We conclude by an opening to the case of symmetric spaces.
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Funding
N. Guigui has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grantagreement G-Statistics No 786854.
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Chevallier, E., Guigui, N. (2021). Wrapped Statistical Models on Manifolds: Motivations, The Case SE(n), and Generalization to Symmetric Spaces. In: Barbaresco, F., Nielsen, F. (eds) Geometric Structures of Statistical Physics, Information Geometry, and Learning. SPIGL 2020. Springer Proceedings in Mathematics & Statistics, vol 361. Springer, Cham. https://doi.org/10.1007/978-3-030-77957-3_5
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DOI: https://doi.org/10.1007/978-3-030-77957-3_5
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