This paper addresses the problem of handling missing not-at-random measurements in matrix completion. This is not a new line of thought in statistics literature, but this paper nicely bridges the ideas to present them to a NeurIPS audience. That said, it seems like the authors are unaware of some key recent work, including those I include below. In their revision, the reviewers must look into and include citations from this literature. Dray, Stéphane, and Julie Josse. "Principal component analysis with missing values: a comparative survey of methods." Plant Ecology 216, no. 5 (2015): 657-667. Steck, Harald. "Training and testing of recommender systems on data missing not at random." In Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 713-722. ACM, 2010. and if the authors are willing to cite very new work that came out this summer: Sportisse, Aude, Claire Boyer, and Julie Josse. "Estimation and imputation in Probabilistic Principal Component Analysis with Missing Not At Random data." (2019). https://arxiv.org/abs/1906.02493