Stochastic development regression using method of moments

Line Kühnel; Stefan Horst Sommer

doi:10.1007/978-3-319-68445-1_1

Stochastic development regression using method of moments

Line Kühnel^*, Stefan Horst Sommer

^*Corresponding author af dette arbejde

Datalogisk Institut

1 Citationer (Scopus)

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.

Originalsprog	Engelsk
Titel	Geometric Science of Information : Third International Conference, GSI 2017, Paris, France, November 7-9, 2017, Proceedings
Redaktører	Frank Nielsen, Fréderic Barbaresco
Antal sider	9
Forlag	Springer
Publikationsdato	2017
Sider	3-11
ISBN (Trykt)	978-3-319-68444-4
ISBN (Elektronisk)	978-3-319-68445-1
DOI	https://doi.org/10.1007/978-3-319-68445-1_1
Status	Udgivet - 2017
Begivenhed	3rd International Conference on Geometric Science of Information - Paris, Frankrig Varighed: 7 nov. 2017 → 9 nov. 2017 Konferencens nummer: 3

Konference

Konference	3rd International Conference on Geometric Science of Information
Nummer	3
Land/Område	Frankrig
By	Paris
Periode	07/11/2017 → 09/11/2017

Navn	Lecture notes in computer science
Vol/bind	10589
ISSN	0302-9743

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10.1007/978-3-319-68445-1_1

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Citationsformater

Stochastic development regression using method of moments. / Kühnel, Line; Sommer, Stefan Horst.
Geometric Science of Information: Third International Conference, GSI 2017, Paris, France, November 7-9, 2017, Proceedings. red. / Frank Nielsen; Fréderic Barbaresco. Springer, 2017. s. 3-11 (Lecture notes in computer science, Bind 10589).

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

Kühnel, L & Sommer, SH 2017, Stochastic development regression using method of moments. i F Nielsen & F Barbaresco (red), Geometric Science of Information: Third International Conference, GSI 2017, Paris, France, November 7-9, 2017, Proceedings. Springer, Lecture notes in computer science, bind 10589, s. 3-11, 3rd International Conference on Geometric Science of Information, Paris, Frankrig, 07/11/2017. https://doi.org/10.1007/978-3-319-68445-1_1

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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.",

keywords = "Frame bundle, Non-linear statistics, Regression, Statistics on manifolds, Stochastic development",

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AB - 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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KW - Non-linear statistics

KW - Regression

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KW - Stochastic development

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Stochastic development regression using method of moments

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