2017/02/02 by Michael Rosenthal, Rosenthal, Michael, Wei Biao Wu +5
Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Morphological variations and asymmetry #Other Statistics (stat.OT) #Scientific Research and Discoveries #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1702.00823
openalex publication_date 2017/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.