Bayesian-Driven Learning of A New Weighted Tensor Norm for Tensor Recovery

Jingjing Zheng, Yankai Cao

Keywords: Tensor Recovery; t-SVD

Abstract: This study addresses the performance limitations of t-SVD-based tensor recovery caused by non-smooth changes and imbalanced low-rankness in tensor data. We introduce a novel bilevel tensor completion model, integrating the learning of a data-dependent weighted tensor norm within the tensor completion framework as an upper-level problem. We treat the optimization of the bilevel problem as a black-box problem, employing Bayesian Optimization (BO) for efficient learning of the proposed tensor norm. Numerical experiments demonstrated the superior performance of our proposed method compared to state-of-the-art methods in tensor completion. The code of our method is available at \url{https://github.com/jzheng20/TR-BO.git}.

Submission Number: 188