Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center
Reviewers are mostly favorable. Quantile regression is used widely and successfully in practice, so giving it stronger theoretical guarantees is worthwhile. The key issue in the less favorable review is in the quote from  by Vovk et al., 1999: "The full conformal and split conformal methods both tend to produce prediction bands C(x) whose width is roughly constant over x in Rd. ... in some scenarios ... the residual variance will vary nontrivially with X, and in such a case we want the conformal band to adapt correspondingly." Heteroskedasticity is an important issue that for 20 years hasn't been addressed fully in the context of conformal prediction. As the reviewer says, "mu(X) can be any regression estimator including the quantile regression proposed in this paper." The contribution of this submission is to work out this idea in detail, which is a good contribution.