Conformalized Unconditional Quantile Regression

Ahmed Alaa, Zeshan Hussain, David Sontag

Abstract:

We develop a predictive inference procedure that
combines conformal prediction (CP) with unconditional quantile regression (QR)—a commonly
used tool in econometrics [1] that involves regressing the recentered influence function (RIF) of
the quantile functional over input covariates. Unlike the more widely-known conditional QR, unconditional QR explicitly captures the impact of
changes in covariate distribution on the quantiles
of the marginal distribution of outcomes. Leveraging this property, our procedure issues adaptive
predictive intervals with localized frequentist coverage guarantees. It operates by fitting a machine
learning model for the RIFs using training data,
and then applying the CP procedure for any test
covariate with respect to a “hypothetical” covariate distribution localized around the new instance.
Experiments show that our procedure is adaptive
to heteroscedasticity, provides transparent coverage guarantees that are relevant to the test instance
at hand, and performs competitively with existing
methods in terms of efficiency.