Nonparametric Spherical Regression Using Diffeomorphic Mappings
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2017-02-06 v1
Abstract
Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map from a sphere to itself. The restriction of this mapping to diffeomorphisms is natural in several settings. The model is estimated in a penalized maximum-likelihood framework using gradient-based optimization. Towards that goal, we specify a first-order roughness penalty using the Jacobian of diffeomorphisms. We compare the prediction performance of the proposed model with state-of-the-art methods using simulated and real data involving cloud deformations, wind directions, and vector-cardiograms. This model is found to outperform others in capturing relationships between spherical variables.
Cite
@article{arxiv.1702.00823,
title = {Nonparametric Spherical Regression Using Diffeomorphic Mappings},
author = {Michael Rosenthal and Wei Wu and Eric Klassen and Anuj Srivastava},
journal= {arXiv preprint arXiv:1702.00823},
year = {2017}
}