Reviews: Blind Regression: Nonparametric Regression for Latent Variable Models via Collaborative Filtering

The authors do a good job of presenting the high-level ideas behind their contribution and presenting the relevant literature in context. The actual contribution is quite technical in nature, but a good amount of effort is taken to walk the reader through it. The authors might also look into approaches like SLIM (Ning and Karypis), which also approach matrix completion tasks using (fairly simple) models that overcome the low-rank assumption of typical matrix completion approaches. Although the paper promises to recover matrix data generated by a quite general class of functions, I struggled to understand which of the operating assumptions (section 2) are actually realistic. In particular, assumption (e) (each entry is observed independently) is certainly violated in the netflix and movielens datasets where the "missing at random" assumption does not hold (as would be the case in any dataset where users self-select what to evaluate; see papers on the "missing not at random" assumption).