Correcting the Coverage Bias of Quantile Regression

Isaac Gibbs, Emmanuel Candes, John Cherian

Abstract:

We develop a collection of methods for adjusting the predictions of quantile regression
to ensure coverage. Our methods are model agnostic and can be used to correct for
high-dimensional overfitting bias with only minimal assumptions. Theoretical results
show that the estimates we develop are consistent and facilitate accurate calibration in
the proportional asymptotic regime where the ratio of the dimension of the data and the
sample size converges to a constant. This is further confirmed by experiments on both
simulated and real data. A key component of our work is a new connection between the
leave-one-out coverage and the fitted values of variables appearing in a dual formulation
of the quantile regression problem. This facilitates the use of cross-validation in a
variety of settings at significantly reduced computational costs.