Uncertainty Quantification for Nonconvex Tensor Completion: Confidence Intervals, Heteroscedasticity and Optimality

Changxiao Cai, H. Vincent Poor, Yuxin Chen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study the distribution and uncertainty of nonconvex optimization for noisy tensor completion-the problem of estimating a low-rank tensor given incomplete and corrupted observations of its entries. Focusing on a two-stage estimation algorithm proposed by Cai et al., we characterize the distribution of this nonconvex estimator down to fine scales. This distributional theory in turn allows one to construct valid and short confidence intervals for both the unseen tensor entries and the unknown tensor factors. The proposed inferential procedure enjoys several important features: (1) it is fully adaptive to noise heteroscedasticity, and (2) it is data-driven and automatically adapts to unknown noise distributions. Furthermore, our findings unveil the statistical optimality of nonconvex tensor completion: it attains un-improvable ℓ2 accuracy-including both the rates and the pre-constants-when estimating both the unknown tensor and the underlying tensor factors.

Original languageEnglish (US)
Pages (from-to)407-452
Number of pages46
JournalIEEE Transactions on Information Theory
Volume69
Issue number1
DOIs
StatePublished - Jan 1 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Library and Information Sciences
  • Computer Science Applications

Keywords

  • Confidence intervals
  • heteroscedasticity
  • nonconvex optimization
  • tensor completion
  • uncertainty quantification

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