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math.OC2021
On Geometric Connections of Embedded and Quotient Geometries in Riemannian Fixed-rank Matrix Optimization
Yuetian Luo, Xudong Li, Anru R. Zhang
In this paper, we propose a general procedure for establishing the geometric landscape connections of a Riemannian optimization problem under the embedded and quotient geometries.…
math.OC2021★ 1 cited
Nonconvex Factorization and Manifold Formulations are Almost Equivalent in Low-rank Matrix Optimization
Yuetian Luo, Xudong Li, Anru R. Zhang
In this paper, we consider the geometric landscape connection of the widely studied manifold and factorization formulations in low-rank positive semidefinite (PSD) and general matr…
stat.ML2021★ 8 cited
Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence
Yuetian Luo, Anru R. Zhang
In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements. The general problem covers many specific examples arising from app…