82 citations · 384 across the 49 of their papers we have counts for
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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.…
Guaranteed Functional Tensor Singular Value Decomposition
Rungang Han, Pixu Shi, Anru R. Zhang
This paper introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one functional mode and several tabular mod…
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…
Learning Good State and Action Representations via Tensor Decomposition
Chengzhuo Ni, Yaqi Duan, Munther Dahleh +2
The transition kernel of a continuous-state-action Markov decision process (MDP) admits a natural tensor structure. This paper proposes a tensor-inspired unsupervised learning meth…
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…