Ridge Regression on Riemannian Manifolds for Time-Series Prediction
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Nava-Yazdani, Esfandiar |
| author_facet | Nava-Yazdani, Esfandiar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ridge Regression on Riemannian Manifolds for Time-Series Prediction Nava-Yazdani, Esfandiar Differential Geometry Numerical Analysis Applications Machine Learning 53B, 53C (Primary), 62, 65D (Secondary) 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. |
| title | Ridge Regression on Riemannian Manifolds for Time-Series Prediction |
| topic | Differential Geometry Numerical Analysis Applications Machine Learning 53B, 53C (Primary), 62, 65D (Secondary) |
| url | https://arxiv.org/abs/2411.18339 |