Distributional conformal prediction

TL;DR

This paper introduces a robust distributional conformal prediction method that constructs conditionally valid prediction intervals using models for conditional distributions, applicable across various prediction tasks and resilient to model misspecification.

Contribution

It develops a novel conformal prediction approach based on probability integral transform and ranks, ensuring conditional validity even under heteroskedasticity and model misspecification.

Findings

Provides approximate conditional validity under consistent estimation.

Ensures unconditional validity under model misspecification and time series data.

Introduces a shape adjustment for optimal prediction intervals.

Abstract

We propose a robust method for constructing conditionally valid prediction intervals based on models for conditional distributions such as quantile and distribution regression. Our approach can be applied to important prediction problems including cross-sectional prediction, k-step-ahead forecasts, synthetic controls and counterfactual prediction, and individual treatment effects prediction. Our method exploits the probability integral transform and relies on permuting estimated ranks. Unlike regression residuals, ranks are independent of the predictors, allowing us to construct conditionally valid prediction intervals under heteroskedasticity. We establish approximate conditional validity under consistent estimation and provide approximate unconditional validity under model misspecification, overfitting, and with time series data. We also propose a simple "shape" adjustment of our baseline method that yields optimal prediction intervals.