Export Reviews, Discussions, Author Feedback and Meta-Reviews

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: This paper studies the Principal Component Analysis (PCA) for large tensors of arbitrary order k under a single-spike model. Solving tensor PCA exactly is in general NP hard. Given a completely observed rank-one symmetric tensor, this paper provides conditions under which one can reliably estimate the unknown unit vector. Specifically, the paper gives conditions on signal-to-noise ratio under several scenarios which allow one to estimate the solution reliably. For the maximum-likelihood estimator (MLE), the authors show that in an ideal case with unbounded computational resources, the MLE is successful with high probability if the signal-to-noise ration is above sqrt(k.log(k))(1+o(1))