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

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Discrete-Time Observations of Brownian Motion on Lie Groups and Homogeneous Spaces : Sampling and Metric Estimation. / Jensen, Mathias Højgaard; Joshi, Sarang; Sommer, Stefan.

In: Algorithms, Vol. 15, No. 8, 290, 2022, p. 1-17.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Jensen, MH, Joshi, S & Sommer, S 2022, 'Discrete-Time Observations of Brownian Motion on Lie Groups and Homogeneous Spaces: Sampling and Metric Estimation', Algorithms, vol. 15, no. 8, 290, pp. 1-17. https://doi.org/10.3390/a15080290

APA

Jensen, M. H., Joshi, S., & Sommer, S. (2022). Discrete-Time Observations of Brownian Motion on Lie Groups and Homogeneous Spaces: Sampling and Metric Estimation. Algorithms, 15(8), 1-17. [290]. https://doi.org/10.3390/a15080290

Vancouver

Jensen MH, Joshi S, Sommer S. Discrete-Time Observations of Brownian Motion on Lie Groups and Homogeneous Spaces: Sampling and Metric Estimation. Algorithms. 2022;15(8):1-17. 290. https://doi.org/10.3390/a15080290

Author

Jensen, Mathias Højgaard ; Joshi, Sarang ; Sommer, Stefan. / Discrete-Time Observations of Brownian Motion on Lie Groups and Homogeneous Spaces : Sampling and Metric Estimation. In: Algorithms. 2022 ; Vol. 15, No. 8. pp. 1-17.

Bibtex

@article{f153e31e87e24a9f8c36ce223b975f9d,
title = "Discrete-Time Observations of Brownian Motion on Lie Groups and Homogeneous Spaces: Sampling and Metric Estimation",
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 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). ",
author = "Jensen, {Mathias H{\o}jgaard} and Sarang Joshi and Stefan Sommer",
year = "2022",
doi = "10.3390/a15080290",
language = "English",
volume = "15",
pages = "1--17",
journal = "Algorithms",
issn = "1999-4893",
publisher = "M D P I AG",
number = "8",

}

RIS

TY - JOUR

T1 - Discrete-Time Observations of Brownian Motion on Lie Groups and Homogeneous Spaces

T2 - Sampling and Metric Estimation

AU - Jensen, Mathias Højgaard

AU - Joshi, Sarang

AU - Sommer, Stefan

PY - 2022

Y1 - 2022

N2 - 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).

AB - 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).

U2 - 10.3390/a15080290

DO - 10.3390/a15080290

M3 - Journal article

VL - 15

SP - 1

EP - 17

JO - Algorithms

JF - Algorithms

SN - 1999-4893

IS - 8

M1 - 290

ER -

ID: 316817429