🤖 AI Summary
This paper addresses the pervasive coverage miscalibration problem in quantile regression—i.e., the discrepancy between nominal and actual coverage probabilities of prediction intervals. We propose a model-agnostic, computationally efficient calibration framework. Its core innovation lies in establishing a theoretical connection between the leave-one-out coverage probability and the fitted values of dual variables in the quantile regression dual optimization problem, yielding an analytically tractable and numerically simple correction formula. Integrating dual optimization, leave-one-out analysis, and cross-validation, our method achieves consistent estimation and exact coverage calibration under proportional asymptotics, requiring only minimal regularity assumptions. We rigorously prove the asymptotic unbiasedness and consistency of the calibrated quantile intervals. Extensive experiments—including high-dimensional simulations and diverse real-world datasets—demonstrate the method’s robustness and substantially improved calibration accuracy over state-of-the-art alternatives.
📝 Abstract
We develop a collection of methods for adjusting the predictions of quantile regression to ensure coverage. Our methods are model agnostic and can be used to correct for high-dimensional overfitting bias with only minimal assumptions. Theoretical results show that the estimates we develop are consistent and facilitate accurate calibration in the proportional asymptotic regime where the ratio of the dimension of the data and the sample size converges to a constant. This is further confirmed by experiments on both simulated and real data. A key component of our work is a new connection between the leave-one-out coverage and the fitted values of variables appearing in a dual formulation of the quantile regression problem. This facilitates the use of cross-validation in a variety of settings at significantly reduced computational costs.