Bridge Simulation and Metric Estimation on Lie Groups

Mathias Højgaard Jensen; Sarang Joshi; Stefan Sommer

doi:10.1007%2F978-3-030-80209-7_47

Bridge Simulation and Metric Estimation on Lie Groups

Mathias Højgaard Jensen, Sarang Joshi, Stefan Sommer

Image Analysis, Computational Modelling and Geometry

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

Abstract

We present a simulation scheme for simulating Brownian bridges on complete and connected Lie groups. We show how this simulation scheme leads to absolute continuity of the Brownian bridge measure with respect to the guided process measure. This result generalizes the Euclidean result of Delyon and Hu to Lie groups. We present numerical results of the guided process in the Lie group SO(3) . In particular, we apply importance sampling to estimate the metric on SO(3) using an iterative maximum likelihood method.

Originalsprog	Engelsk
Titel	Geometric Science of Information : 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings
Forlag	Springer
Publikationsdato	2021
Sider	430-438
DOI	https://doi.org/10.1007%2F978-3-030-80209-7_47
Status	Udgivet - 2021
Begivenhed	5th conference on Geometric Science of Information - GSI2021 - Paris, Frankrig Varighed: 21 jul. 2021 → 23 jul. 2021

Konference

Konference	5th conference on Geometric Science of Information - GSI2021
Land/Område	Frankrig
By	Paris
Periode	21/07/2021 → 23/07/2021

Navn	Lecture Notes in Computer Science
Vol/bind	12829
ISSN	0302-9743

Adgang til dokumentet

10.1007%2F978-3-030-80209-7_47

https://arxiv.org/pdf/2106.03431.pdfLicens: CC BY

Citationsformater

Bridge Simulation and Metric Estimation on Lie Groups. / Højgaard Jensen, Mathias; Joshi, Sarang; Sommer, Stefan.

Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings. Springer, 2021. s. 430-438 (Lecture Notes in Computer Science, Bind 12829).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

Højgaard Jensen, M, Joshi, S & Sommer, S 2021, Bridge Simulation and Metric Estimation on Lie Groups. i Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings. Springer, Lecture Notes in Computer Science, bind 12829, s. 430-438, 5th conference on Geometric Science of Information - GSI2021, Paris, Frankrig, 21/07/2021. https://doi.org/10.1007%2F978-3-030-80209-7_47

@inproceedings{49e514ac6aaa4c9895dafbe75ec747ce,

title = "Bridge Simulation and Metric Estimation on Lie Groups",

abstract = "We present a simulation scheme for simulating Brownian bridges on complete and connected Lie groups. We show how this simulation scheme leads to absolute continuity of the Brownian bridge measure with respect to the guided process measure. This result generalizes the Euclidean result of Delyon and Hu to Lie groups. We present numerical results of the guided process in the Lie group SO(3) . In particular, we apply importance sampling to estimate the metric on SO(3) using an iterative maximum likelihood method.",

author = "{H{\o}jgaard Jensen}, Mathias and Sarang Joshi and Stefan Sommer",

year = "2021",

doi = "10.1007%2F978-3-030-80209-7_47",

language = "English",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "430--438",

booktitle = "Geometric Science of Information",

address = "Switzerland",

note = "5th conference on Geometric Science of Information - GSI2021 ; Conference date: 21-07-2021 Through 23-07-2021",

}

TY - GEN

T1 - Bridge Simulation and Metric Estimation on Lie Groups

AU - Højgaard Jensen, Mathias

AU - Joshi, Sarang

AU - Sommer, Stefan

PY - 2021

Y1 - 2021

N2 - We present a simulation scheme for simulating Brownian bridges on complete and connected Lie groups. We show how this simulation scheme leads to absolute continuity of the Brownian bridge measure with respect to the guided process measure. This result generalizes the Euclidean result of Delyon and Hu to Lie groups. We present numerical results of the guided process in the Lie group SO(3) . In particular, we apply importance sampling to estimate the metric on SO(3) using an iterative maximum likelihood method.

AB - We present a simulation scheme for simulating Brownian bridges on complete and connected Lie groups. We show how this simulation scheme leads to absolute continuity of the Brownian bridge measure with respect to the guided process measure. This result generalizes the Euclidean result of Delyon and Hu to Lie groups. We present numerical results of the guided process in the Lie group SO(3) . In particular, we apply importance sampling to estimate the metric on SO(3) using an iterative maximum likelihood method.

U2 - 10.1007%2F978-3-030-80209-7_47

DO - 10.1007%2F978-3-030-80209-7_47

M3 - Article in proceedings

T3 - Lecture Notes in Computer Science

SP - 430

EP - 438

BT - Geometric Science of Information

PB - Springer

T2 - 5th conference on Geometric Science of Information - GSI2021

Y2 - 21 July 2021 through 23 July 2021

ER -