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Geometric Integration of Measure-Preserving Flows for Sampling

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Geometric Structures of Statistical Physics, Information Geometry, and Learning (SPIGL 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 361))

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Abstract

Many of the state-of-the-art Monte Carlo sampling algorithms are inspired by Hamiltonian Monte Carlo and constructed from measure-preserving Langevin diffusions through an appropriate geometric integrator. In this article, following [9] we discuss the general construction of such Hamiltonian-based samplers starting from the canonical recipe of measure-preserving diffusions. Moreover, we discuss the properties that make Hamiltonian mechanics particularly appropriate to devise efficient Monte Carlo methods.

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Authors and Affiliations

  1. The Alan Turing Instituted and Department of Engineering, The University of Cambridge, Cambridge, CB3 0FA, UK

    Alessandro Barp

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  1. Alessandro Barp
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  1. Thales Land & Air Systems, Technical Directorate, Thales, Limours, France

    Frédéric Barbaresco

  2. Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

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Barp, A. (2021). Geometric Integration of Measure-Preserving Flows for Sampling. In: Barbaresco, F., Nielsen, F. (eds) Geometric Structures of Statistical Physics, Information Geometry, and Learning. SPIGL 2020. Springer Proceedings in Mathematics & Statistics, vol 361. Springer, Cham. https://doi.org/10.1007/978-3-030-77957-3_18

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