  Conformal prediction is a technique for constructing prediction intervals
that attain valid coverage in finite samples, without making distributional
assumptions. Despite this appeal, existing conformal methods can be
unnecessarily conservative because they form intervals of constant or weakly
varying length across the input space. In this paper we propose a new method
that is fully adaptive to heteroscedasticity. It combines conformal prediction
with classical quantile regression, inheriting the advantages of both. We
establish a theoretical guarantee of valid coverage, supplemented by extensive
experiments on popular regression datasets. We compare the efficiency of
conformalized quantile regression to other conformal methods, showing that our
method tends to produce shorter intervals.
