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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. SUMMARY This paper proposes a nuclear norm penalized estimator for matrix completion problem, where the observations take a finite (discrete) number of values. Both with theoretical analysis and with numerical experiment, the authors verify the proposed approach is effective. I understand that there are cases where the observations are discrete and that we may need a distinguished algorithm for them, the recommendation systems may not be a good example. Although most recommender system datasets allow finite number of possible ratings (usually 1 to 5 stars), the output does not need to be finite.