Jul 12, 2020
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 nonconvex estimation algorithm, we characterize the distribution of this 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 its underlying tensor factors. The proposed inferential procedure enjoys several important features: (1) it is fully adaptive to noise heteroscedasticity; (2) it is data-driven and adapts automatically to unknown noise distributions. Furthermore, our findings unveil the statistical optimality of nonconvex tensor completion: it attains un-improvable estimation accuracy — including both the rates and the pre-constants — under i.i.d. Gaussian noise.
The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.
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