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.

中文翻译：

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通过自我验证的张量完成模型的最优性验证

张量完成 (TC) 尝试从部分观察中估计缺失的张量条目。在过去的十年中，大量的工作都集中在这个问题上，从而产生了一些优秀的 TC 方法。因此，一个关键的问题是如何验证 TC 模型的最优性，尤其是当底层张量未知时，这是实践中的常见场景。唯一可用的现有方法——数据验证——解决了基于验证集的问题。虽然简单，但这种方法可能会导致模型非最优，尤其是在缺失率和噪声较高的情况下。在这项工作中，我们提出了一种自我验证方法，该方法考虑了一个名为可识别性度量的度量，该度量基于张量情况下的异构条件的泛化定义。值得注意的是，可识别性度量可以在不使用任何验证集的情况下验证 TC 模型的最优性。在合成数据集和真实数据集上进行的大量数值实验凭经验验证了所提出的方法相对于数据验证方法的优越性。