Jiuqian Shang | Searcharxiv

arXiv2026

Uncertainty Quantification for Noisy Low-tubal-rank Tensor Completion

High-dimensional tensor data often exhibit strong temporal correlations that appear as low-dimensional structures in the frequency domain. While the low-tubal-rank tensor model effectively captures these spectral features, making it potentially suitable for geophysical data, existing methods primarily focus on point estimation. Uncertainty quantification (UQ) of imputed values and rigorous statistical inference for these models remain largely unexplored. In this work, we propose a flexible inference framework for linear forms of high-dimensional tensors. Employing a double-sample debiasing technique followed by a low-rank projection, we construct asymptotically Gaussian estimators that yield valid statistical inference under mild assumptions. More precisely, we can perform hypothesis testing and construct confidence intervals with this result. We validate the theoretical results through extensive simulations and demonstrate the practical effectiveness of our method in completing the global total electron content data. We demonstrate, using those numerical results, that our entrywise confidence intervals are robust and reliable, yielding informative uncertainty quantification that captures underlying variability.

stat.ME↗

arXiv2025

Fourier Low-rank and Sparse Tensor for Efficient Tensor Completion

Tensor completion is crucial in many scientific domains with missing data problems. Traditional low-rank tensor models, including CP, Tucker, and Tensor-Train, exploit low-dimensional structures to recover missing data. However, these methods often treat all tensor modes symmetrically, failing to capture the unique spatiotemporal patterns inherent in scientific data, where the temporal component exhibits both low-frequency stability and high-frequency variations. To address this, we propose a novel model, \underline{F}ourier \underline{Lo}w-rank and \underline{S}parse \underline{T}ensor (FLoST), which decomposes the tensor along the temporal dimension using a Fourier transform. This approach captures low-frequency components with low-rank matrices and high-frequency fluctuations with sparsity, resulting in a hybrid structure that efficiently models both smooth and localized variations. Compared to the well-known tubal-rank model, which assumes low-rankness across all frequency components, FLoST requires significantly fewer parameters, making it computationally more efficient, particularly when the time dimension is large. Through theoretical analysis and empirical experiments, we demonstrate that FLoST outperforms existing tensor completion models in terms of both accuracy and computational efficiency, offering a more interpretable solution for spatiotemporal data reconstruction.

cs.LG↗