Uncertainty Quantification for Noisy Low-tubal-rank Tensor Completion

2026-04-11

AI Summary

This study addresses the lack of uncertainty quantification and statistical inference methods for high-dimensional tensor completion. Focusing on low tubal-rank tensor completion, the work proposes the first framework enabling rigorous statistical inference by constructing asymptotically Gaussian estimators through two-sample debiasing, low-rank projection, and frequency-domain low tubal-rank modeling. This approach facilitates element-wise confidence intervals and hypothesis testing. Theoretical analysis establishes the asymptotic normality and statistical validity of the proposed estimator. Experiments on both synthetic data and real-world global ionospheric total electron content measurements demonstrate that the resulting confidence intervals are robust and reliably capture the intrinsic variability of the data.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Uncertainty Quantification
• Low-tubal-rank Tensor Completion
• Statistical Inference
• High-dimensional Tensor Data

Innovation

• uncertainty quantification
• low-tubal-rank tensor
• statistical inference
• double-sample debiasing
• confidence intervals