Stochastic development regression using method of moments
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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. ed. / Frank Nielsen; Fréderic Barbaresco. Springer, 2017. p. 3-11 (Lecture notes in computer science, Vol. 10589).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - Stochastic development regression using method of moments
AU - Kühnel, Line
AU - Sommer, Stefan Horst
N1 - Conference code: 3
PY - 2017
Y1 - 2017
N2 - 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.
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.
KW - Frame bundle
KW - Non-linear statistics
KW - Regression
KW - Statistics on manifolds
KW - Stochastic development
UR - http://www.scopus.com/inward/record.url?scp=85033693692&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-68445-1_1
DO - 10.1007/978-3-319-68445-1_1
M3 - Article in proceedings
AN - SCOPUS:85033693692
SN - 978-3-319-68444-4
T3 - Lecture notes in computer science
SP - 3
EP - 11
BT - Geometric Science of Information
A2 - Nielsen, Frank
A2 - Barbaresco, Fréderic
PB - Springer
Y2 - 7 November 2017 through 9 November 2017
ER -
ID: 188481061