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Bridge Simulation and Metric Estimation on Lie Groups

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Geometric Science of Information (GSI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12829))

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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 \(\mathrm {SO}(3)\). In particular, we apply importance sampling to estimate the metric on \(\mathrm {SO}(3)\) using an iterative maximum likelihood method.

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Correspondence to Mathias Højgaard Jensen .

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Jensen, M.H., Joshi, S., Sommer, S. (2021). Bridge Simulation and Metric Estimation on Lie Groups. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_47

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  • DOI: https://doi.org/10.1007/978-3-030-80209-7_47

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-80208-0

  • Online ISBN: 978-3-030-80209-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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