# Ridge Regression on Riemannian Manifolds for Time-Series Prediction

arXiv: https://arxiv.org/abs/2411.18339 · HTML: https://mlsanity.com/paper/2411.18339/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 27 Nov 2024.

## Builds on (most cited first, 4 of 4)

- [Predicting Hurricane Trajectories using a Recurrent Neural Network](https://mlsanity.com/paper/1802.02548/) (2018)
- [Geodesic analysis in Kendall's shape space with epidemiological applications](https://mlsanity.com/paper/1906.11950/) (2019)
- [A Hierarchical Geodesic Model for Longitudinal Analysis on Manifolds](https://mlsanity.com/paper/2111.15371/) (2021)
- [Sasaki Metric for Spline Models of Manifold-Valued Trajectories](https://mlsanity.com/paper/2303.17299/) (2023)

## Built on by (most cited first, 1 of 1)

- [SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting](https://mlsanity.com/paper/2606.09917/) (2026)

## Abstract (arXiv)

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 B'ezier 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.