Distributional conformal prediction

Abstract

<jats:title>Significance</jats:title> <jats:p>Prediction problems are important in many contexts. Examples include cross-sectional prediction, time series forecasting, counterfactual prediction and synthetic controls, and individual treatment effect prediction. We develop a prediction method that works in conjunction with many powerful classical methods (e.g., conventional quantile regression) as well as modern high-dimensional methods for estimating conditional distributions (e.g., quantile neural networks). Unlike many existing prediction approaches, our method is valid conditional on the observed predictors and efficient under some conditions. Importantly, our method is also robust; it exhibits unconditional coverage guarantees under model misspecification, under overfitting, and with time series data.</jats:p>