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.
| Original language | English |
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| Title of host publication | Geometric Science of Information : Third International Conference, GSI 2017, Paris, France, November 7-9, 2017, Proceedings |
| Editors | Frank Nielsen, Fréderic Barbaresco |
| Number of pages | 9 |
| Publisher | Springer |
| Publication date | 2017 |
| Pages | 3-11 |
| ISBN (Print) | 978-3-319-68444-4 |
| ISBN (Electronic) | 978-3-319-68445-1 |
| DOIs | |
| Publication status | Published - 2017 |
| Event | 3rd International Conference on Geometric Science of Information - Paris, France Duration: 7 Nov 2017 → 9 Nov 2017 Conference number: 3 |
Conference
| Conference | 3rd International Conference on Geometric Science of Information |
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| Number | 3 |
| Country/Territory | France |
| City | Paris |
| Period | 07/11/2017 → 09/11/2017 |
| Series | Lecture notes in computer science |
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| Volume | 10589 |
| ISSN | 0302-9743 |
Keywords
- Frame bundle
- Non-linear statistics
- Regression
- Statistics on manifolds
- Stochastic development