Reviews: Missing Not at Random in Matrix Completion: The Effectiveness of Estimating Missingness Probabilities Under a Low Nuclear Norm Assumption

Since the algorithm of estimating the propensity is proposed by Davenport et al. 2014, the originality of the paper mainly lies in the bounds derivation and experiments. For the bounds of the bias and overall completion error, there is no direct experiments bridging the proposed theory and practice. I would like more empirical evidences on the assumptions from real-world matrices, beyond the recommendation domain where COAT and MovieLens are from. The novelty of the paper is also less impressive when the motivation of investigating the adoption of nuclear norm is unclear. From the experiments, it is only demonstrated that the proposed propensity estimator can achieve similar results as previous classic methods (and can be even slightly worse if data fits better for Naive Bayes or Logistic Regression). The performance gain of the newly proposed estimator on the MovieLens dataset (the largest experimented datasets) is not very significant compared with Naive Bayes, meaning that when m and n are large the bias and completion error is similar to Naive Bayes.