An Optimal Statistical and Computational Framework for Generalized Tensor Estimation

Understand

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis.

• The proposed estimator consists of finding a low-rank tensor fit to the data under generalized parametric models.
• To overcome the difficulty of non-convexity in these problems, we introduce a unified approach of projected gradient descent that adapts to the underlying low-rank structure.
• Under mild conditions on the loss function, we establish both an upper bound on statistical error and the linear rate of computational convergence through a general deterministic analysis.