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- W4308351880 abstract "We present schemes for simulating Brownian bridges on complete and connected Lie groups and homogeneous spaces. We use this to construct an estimation scheme for recovering an unknown left- or right-invariant Riemannian metric on the Lie group from samples. We subsequently show how pushing forward the distributions generated by Brownian motions on the group results in distributions on homogeneous spaces that exhibit non-trivial covariance structure. The pushforward measure gives rise to new parametric families of distributions on commonly occurring spaces such as spheres and symmetric positive tensors. We extend the estimation scheme to fit these distributions to homogeneous space-valued data. We demonstrate both the simulation schemes and estimation procedures on Lie groups and homogenous spaces, including $SPD(3) = GL_+(3)/SO(3)$ and $mathbb S^2 = SO(3)/SO(2)$." @default.
- W4308351880 created "2022-11-11" @default.
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- W4308351880 date "2021-12-01" @default.
- W4308351880 modified "2023-09-24" @default.
- W4308351880 title "Bridge Simulation and Metric Estimation on Lie Groups and Homogeneous Spaces" @default.
- W4308351880 doi "https://doi.org/10.48550/arxiv.2112.00866" @default.
- W4308351880 hasPublicationYear "2021" @default.
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