11: Statistical Inference and Uncertainty Quantification for Noisy Low-Tubal-Rank Tensor Completion

Music City Center 

The low-tubal-rank tensor model has been used for real-world multidimensional data to capture signals in the frequency domain. Algorithms have been developed to estimate low-rank third-order tensors from partial and corrupted entries. However, uncertainty quantification and statistical inference for these estimates remain largely unclear.

Our work addresses this gap. We introduce a flexible framework for making inferences about general linear forms of a large tensor whenever an entry-wise consistent estimator is available. Under mild regularity conditions, we construct asymptotically normal estimators of these linear forms through double-sample debiasing and low-rank projection. These estimators allow us to construct confidence intervals and perform hypothesis testing. Simulation studies support our theoretical results, and we apply the method to the total electron content (TEC) reconstruction problem.

tensor completion

uncertainty quantification

tubal rank

Total Electron Content (TEC) 

IMS