{"ID":2861909,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.00569","arxiv_id":"2510.00569","title":"Guaranteed Noisy CP Tensor Recovery via Riemannian Optimization on the Segre Manifold","abstract":"Recovering a low-CP-rank tensor from noisy linear measurements is a central challenge in high-dimensional data analysis, with applications spanning tensor PCA, tensor regression, and beyond. We exploit the intrinsic geometry of rank-one tensors by casting the recovery task as an optimization problem over the Segre manifold, the smooth Riemannian manifold of rank-one tensors. This geometric viewpoint yields two powerful algorithms: Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN), each of which preserves feasibility at every iteration. Under mild noise assumptions, we prove that RGD converges at a local linear rate, while RGN exhibits an initial local quadratic convergence phase that transitions to a linear rate as the iterates approach the statistical noise floor. Extensive synthetic experiments validate these convergence guarantees and demonstrate the practical effectiveness of our methods.","short_abstract":"Recovering a low-CP-rank tensor from noisy linear measurements is a central challenge in high-dimensional data analysis, with applications spanning tensor PCA, tensor regression, and beyond. We exploit the intrinsic geometry of rank-one tensors by casting the recovery task as an optimization problem over the Segre mani...","url_abs":"https://arxiv.org/abs/2510.00569","url_pdf":"https://arxiv.org/pdf/2510.00569v1","authors":"[\"Ke Xu\",\"Yuefeng Han\"]","published":"2025-10-01T06:44:52Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.OC\",\"math.ST\",\"stat.ME\"]","methods":"[]","has_code":false}