Uncertainty Quantification for Nonconvex Tensor Completion: Confidence Intervals, Heteroscedasticity and Optimality
Uncertainty Quantification for Nonconvex Tensor Completion: Confidence Intervals, Heteroscedasticity and Optimality
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DOI：
10.1109/tit.2022.3205781
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发表时间：
2020-06
影响因子：
2.5
通讯作者：
Changxiao Cai;H. Poor;Yuxin Chen
中科院分区：
文献类型：
--
作者：
Changxiao Cai;H. Poor;Yuxin Chen
我们研究了噪声张量完成的非凸优化的分布和不确定性 - 估计量张量低的问题，鉴于其条目的不完整和损坏的观察结果。该非convex估计器的分布又依次将其构造未知的张量因素。 NONCOVEX TENSOR完成：它达到了不可证明的$ \ ell _ {2} $精度 - 包括速率和预组成者，当时估计了未知的张量和基础张量因子。
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 $\ell _{2}$ accuracy—including both the rates and the pre-constants—when estimating both the unknown tensor and the underlying tensor factors.