On Accuracy and Speed of Geodesic Regression: Do Geometric Priors Improve Learning on Small Datasets?

Adele Myers, Nina Miolane; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2024, pp. 2714-2722

Image datasets in specialized fields of science such as biomedicine are typically smaller than traditional machine learning datasets. As such they present a problem for training many models. To address this challenge researchers often attempt to incorporate priors i.e. external knowledge to help the learning procedure. Geometric priors for example offer to restrict the learning process to the manifold to which the data belong. However learning on manifolds is sometimes computationally intensive to the point of being prohibitive. Here we ask a provocative question: is machine learning on manifolds really more accurate than its linear counterpart to the extent that it is worth sacrificing significant speedup in computation? We answer this question through an extensive theoretical and experimental study of one of the most common learning methods for manifold-valued data: geodesic regression.