Optimality Verification of Tensor Completion Model via Self-Validation

Tensor completion (TC) attempts to estimate the missing tensor entries from partial observations. Over the past decade, a tremendous amount of work has focused on this problem, which has given rise to a few excellent TC methods. Thus, a critical question is how to verify the optimality of TC models, especially when the underlying tensor is unknown, which is a common scenario in practice. The only existing method available—data validation—addresses the problem based on the validation set. While straightforward, this method may lead to a nonoptimal model, especially in scenarios with high missing ratios, and noise. In this work, we propose a self-validation method, which accounts for a metric named the identifiability measure, defined based on the generalization of isomeric conditions in the tensor case. It is noteworthy that the identifiability measure can verify the optimality of TC models without the use of any validation set. Extensive numerical experiments conducted on both synthetic, and real-world datasets empirically validate the superiority of the proposed method over the data validation approach.