Reviews: Towards a Zero-One Law for Column Subset Selection

As a caveat, I am not an expert in the literature surrounding low-rank reconstruction, and may not be entirely correct in my evaluation of the originality and significance of the contributions. Originality:This paper builds upon previous work, in particular [62], which developed column-subset selection for low-rank approximation under the l_p norm. This paper expands upon [62], obtaining results for a broader class of functions and furthermore tightening and fixing some results from [62]. These expansions seem very valuable to the machine learning community. However, the authors may want to further motivate their work by providing specific examples of loss functions to which they extend previous theory, and which have found successful applications in machine learning.