Details

Autor(en) / Beteiligte

• Jensen, Mathias Højgaard
• Joshi, Sarang
• Sommer, Stefan

Titel

Discrete-Time Observations of Brownian Motion on Lie Groups and Homogeneous Spaces: Sampling and Metric Estimation

Ist Teil von

• Algorithms, 2022-08, Vol.15 (8), p.290

Ort / Verlag

Basel: MDPI AG

Erscheinungsjahr

2022

Link zum Volltext

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• 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 a non-trivial covariance structure. The pushforward measure gives rise to new non-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 S2=SO(3)/SO(2).