发表机构
Texas A&M University（德克萨斯农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对张量条目部分已知且低阶ANOVA项占主导的情况，提出基于FFT的存储友好方法，实现最坏情况下的张量完备化，并在合成与真实数据上验证了准确性与可扩展性。
AI 中文摘要
本文从最坏情况的角度处理从张量条目的不完全知识中完备化张量的问题，基于张量的低阶ANOVA项占主导地位这一现实假设。我们调查并利用最优恢复领域的一些近期通用结果，在理论层面提供解决方案。但伴随的最优完备化过程的构造，通常涉及半定规划，由于涉及的巨大维度，在张量情况下不能直接应用。为解决此问题，我们提出一种基于快速傅里叶变换（FFT）的存储友好方法来生成低阶ANOVA投影，同时利用完备化问题的特性来高效计算正则化器和极值特征值。在合成张量和真实世界数据集上的数值实验证明了我们基于FFT的方法的准确性和可扩展性。
英文摘要
In this article, the problem of completing a tensor from some incomplete knowledge of its entries is treated by adopting a worst-case perspective, given the realistic assumption that the tensor's low-order ANOVA terms are dominant. We survey and leverage some recent all-purpose results from the field of Optimal Recovery to provide solutions on a theoretical level. But the accompanying constructions of optimal completion procedures, which often feature semidefinite programs, are not directly applicable in the tensor case due to the huge dimensions involved. To resolve the issue, we put forward a storage-friendly way to produce low-order ANOVA projections based on the fast Fourier transform (FFT), while exploiting the specificities of the completion problem to efficiently compute regularizers and extremal eigenvalues. Numerical experiments on synthetic tensors and real-world datasets demonstrate the accuracy and scalability of our FFT-based method.
