Exact Tensor Completion Beyond Isotropy and Invertibility

Li Ge, Lin Chen, Yudong Chen, Xue Jiang
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:4897-4905, 2026.

Abstract

In this work, a tensor completion problem is studied, which aims to perfectly recover the tensor from partial observations. The existing theoretical guarantee requires the involved transform to be orthogonal, which hinders its applications. In this paper, jumping out of the constraints of isotropy and invertibility for the first time, the theoretical guarantee of exact tensor completion with arbitrary linear transforms is established by directly operating the tensors in the transform domain. With the enriched choices of transforms, we theoretically disclose why slim transforms outperform their square counterparts, providing support for existing works on experimental excellence of slim transforms. Our model and analysis greatly enhance the flexibility of tensor completion, supported by extensive experimental results.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-ge26a, title = { Exact Tensor Completion Beyond Isotropy and Invertibility }, author = {Ge, Li and Chen, Lin and Chen, Yudong and Jiang, Xue}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {4897--4905}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/ge26a/ge26a.pdf}, url = {https://proceedings.mlr.press/v300/ge26a.html}, abstract = { In this work, a tensor completion problem is studied, which aims to perfectly recover the tensor from partial observations. The existing theoretical guarantee requires the involved transform to be orthogonal, which hinders its applications. In this paper, jumping out of the constraints of isotropy and invertibility for the first time, the theoretical guarantee of exact tensor completion with arbitrary linear transforms is established by directly operating the tensors in the transform domain. With the enriched choices of transforms, we theoretically disclose why slim transforms outperform their square counterparts, providing support for existing works on experimental excellence of slim transforms. Our model and analysis greatly enhance the flexibility of tensor completion, supported by extensive experimental results. } }
Endnote
%0 Conference Paper %T Exact Tensor Completion Beyond Isotropy and Invertibility %A Li Ge %A Lin Chen %A Yudong Chen %A Xue Jiang %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-ge26a %I PMLR %P 4897--4905 %U https://proceedings.mlr.press/v300/ge26a.html %V 300 %X In this work, a tensor completion problem is studied, which aims to perfectly recover the tensor from partial observations. The existing theoretical guarantee requires the involved transform to be orthogonal, which hinders its applications. In this paper, jumping out of the constraints of isotropy and invertibility for the first time, the theoretical guarantee of exact tensor completion with arbitrary linear transforms is established by directly operating the tensors in the transform domain. With the enriched choices of transforms, we theoretically disclose why slim transforms outperform their square counterparts, providing support for existing works on experimental excellence of slim transforms. Our model and analysis greatly enhance the flexibility of tensor completion, supported by extensive experimental results.
APA
Ge, L., Chen, L., Chen, Y. & Jiang, X.. (2026). Exact Tensor Completion Beyond Isotropy and Invertibility . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:4897-4905 Available from https://proceedings.mlr.press/v300/ge26a.html.

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