Beyond Global Designs: Low-Rank Tensor Regression with Local-Access Designs

Tongle Wu

The Pennsylvania State University

2026年1月14日 星期三

上午 10:00-11:00

腾讯会议：907-298-430

https://meeting.tencent.com/dm/42JXce0JAlQk

Conventional low-rank tensor regression implicitly assumes a global design: each response is generated by a full inner product between a tensor covariate and an unknown low-rank coefficient tensor. This can be impractical when covariates are high-dimensional or when only partial access to the coefficient tensor is available in distributed, streaming, or privacy-constrained settings.

Motivated by these limitations, in this talk, I will introduce local-access design tensor regression, where each observation is formed from an inner product between a localized subset of the coefficient tensor and a low-dimensional covariate. Focusing on third-order tensors, I introduce two Gaussian local-access design families: slice-wise and tube-wise local designs, respectively. For both settings, we formulate nonconvex estimators and provide statistical and computational guarantees.

Specifically, for slice-wise designs, we prove that alternating exact minimization and projected gradient descent method achieves exact recovery with local linear convergence under reduced sample complexity, and that a preconditioned variant removes dependence on the condition number of the coefficient to accelerate convergence. For tube-wise designs, we utilize the leave-one-out technique to prove that vanilla GD from a spectral initialization has implicit regularization to achieve a linear convergence rate under improved sample complexity. Overall, local-access designs provide provable memory, scalability, and sample-efficiency benefits for high-dimensional tensor regression.