Ridge Regression on Riemannian Manifolds for Time-Series Prediction

2024/11/27 by Esfandiar Nava-Yazdani, Nava-Yazdani, Esfandiar
Computer Science · Decision Sciences · Mathematics · #53B #53C (Primary) #62 #65D (Secondary) #Applications (stat.AP) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Grey System Theory Applications #Machine Learning (stat.ML) #Neural Networks and Applications #Numerical Analysis (math.NA) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2411.18339

openalex publication_date 2024/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We propose a natural intrinsic extension of ridge regression from Euclidean spaces to general Riemannian manifolds for time-series prediction. Our approach combines Riemannian least-squares fitting via Bézier curves, empirical covariance on manifolds, and Mahalanobis distance regularization. A key technical contribution is an explicit formula for the gradient of the objective function using adjoint differentials, enabling efficient numerical optimization via Riemannian gradient descent. We validate our framework through synthetic spherical experiments (achieving significant error reduction over unregularized regression) and hurricane forecasting.

Related

• Manifold-based time series forecasting
• Robust Geodesic Regression
• Local Fréchet Regression with Riemannian Predictors
• A Riemannian Factor Model for Manifold-Valued Time Series
• Conformal inference for regression on Riemannian Manifolds