A comparison of some conformal quantile regression methods
This work addresses the problem of producing locally adaptive prediction intervals for statisticians and machine learning practitioners, but it is incremental as it compares existing methods.
The paper compares two conformal quantile regression methods for prediction intervals, proving their asymptotic efficiency and showing that Romano et al.'s method yields tighter intervals in finite samples.
We compare two recently proposed methods that combine ideas from conformal inference and quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano et al., 2019; Kivaranovic et al., 2019). First, we prove that these two approaches are asymptotically efficient in large samples, under some additional assumptions. Then we compare them empirically on simulated and real data. Our results demonstrate that the method in Romano et al. (2019) typically yields tighter prediction intervals in finite samples. Finally, we discuss how to tune these procedures by fixing the relative proportions of observations used for training and conformalization.