Regression Uncertainty on the Grassmannian

Yi Hong, Xiao Yang, Roland Kwitt, Martin Styner, Marc Niethammer
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:785-793, 2017.

Abstract

Trends in longitudinal or cross-sectional studies over time are often captured through regression models. In their simplest manifestation, these regression models are formulated in $R^n$. However, in the context of imaging studies, the objects of interest which are to be regressed are frequently best modeled as elements of a Riemannian manifold. Regression on such spaces can be accomplished through geodesic regression. This paper develops an approach to compute confidence intervals for geodesic regression models. The approach is general, but illustrated and specifically developed for the Grassmann manifold, which allows us, e.g., to regress shapes or linear dynamical systems. Extensions to other manifolds can be obtained in a similar manner. We demonstrate our approach for regression with 2D/3D shapes using synthetic and real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-hong17b, title = {{Regression Uncertainty on the Grassmannian}}, author = {Hong, Yi and Yang, Xiao and Kwitt, Roland and Styner, Martin and Niethammer, Marc}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {785--793}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/hong17b/hong17b.pdf}, url = {https://proceedings.mlr.press/v54/hong17b.html}, abstract = {Trends in longitudinal or cross-sectional studies over time are often captured through regression models. In their simplest manifestation, these regression models are formulated in $R^n$. However, in the context of imaging studies, the objects of interest which are to be regressed are frequently best modeled as elements of a Riemannian manifold. Regression on such spaces can be accomplished through geodesic regression. This paper develops an approach to compute confidence intervals for geodesic regression models. The approach is general, but illustrated and specifically developed for the Grassmann manifold, which allows us, e.g., to regress shapes or linear dynamical systems. Extensions to other manifolds can be obtained in a similar manner. We demonstrate our approach for regression with 2D/3D shapes using synthetic and real data.} }
Endnote
%0 Conference Paper %T Regression Uncertainty on the Grassmannian %A Yi Hong %A Xiao Yang %A Roland Kwitt %A Martin Styner %A Marc Niethammer %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-hong17b %I PMLR %P 785--793 %U https://proceedings.mlr.press/v54/hong17b.html %V 54 %X Trends in longitudinal or cross-sectional studies over time are often captured through regression models. In their simplest manifestation, these regression models are formulated in $R^n$. However, in the context of imaging studies, the objects of interest which are to be regressed are frequently best modeled as elements of a Riemannian manifold. Regression on such spaces can be accomplished through geodesic regression. This paper develops an approach to compute confidence intervals for geodesic regression models. The approach is general, but illustrated and specifically developed for the Grassmann manifold, which allows us, e.g., to regress shapes or linear dynamical systems. Extensions to other manifolds can be obtained in a similar manner. We demonstrate our approach for regression with 2D/3D shapes using synthetic and real data.
APA
Hong, Y., Yang, X., Kwitt, R., Styner, M. & Niethammer, M.. (2017). Regression Uncertainty on the Grassmannian. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:785-793 Available from https://proceedings.mlr.press/v54/hong17b.html.

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