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Stochastic Development Regression Using Method of Moments

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Geometric Science of Information (GSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

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Abstract

This paper considers the estimation problem arising when inferring parameters in the stochastic development regression model for manifold valued non-linear data. Stochastic development regression captures the relation between manifold-valued response and Euclidean covariate variables using the stochastic development construction. It is thereby able to incorporate several covariate variables and random effects. The model is intrinsically defined using the connection of the manifold, and the use of stochastic development avoids linearizing the geometry. We propose to infer parameters using the Method of Moments procedure that matches known constraints on moments of the observations conditional on the latent variables. The performance of the model is investigated in a simulation example using data on finite dimensional landmark manifolds.

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Acknowledgements

This work was supported by the CSGB Centre for Stochastic Geometry and Advanced Bioimaging funded by a grant from the Villum foundation.

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Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen, Copenhagen, Denmark

    Line Kühnel & Stefan Sommer

Authors
  1. Line Kühnel
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  2. Stefan Sommer
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Correspondence to Line Kühnel .

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Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

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Kühnel, L., Sommer, S. (2017). Stochastic Development Regression Using Method of Moments. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_1

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_1

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  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

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