Reviews: Unbiased estimates for linear regression via volume sampling

I could go either way on this paper, though am slightly positive. The short summary is that the submission gives elegant expectation bounds with non-trivial arguments, but if one wants constant factor approximations (or 1 eps)-approximations), then existing algorithms are faster and read fewer labels. So it's unclear to me if there is a solid application of the results in the paper. In more detail: On the positive side it's great to see an unbiased estimator of the pseudoinverse by volume sampling, which by linearity gives an unbiased estimator to the least squares solution vector. I haven't seen such a statement before. It's also nice to see an unbiased estimator of the least squares loss function when exactly d samples are taken.