Multi-Fidelity Quantile Regression

2026-05-11

AI Summary

High-fidelity data scarcity limits the accuracy of conditional quantile estimation. This work proposes a two-stage, model-agnostic multi-fidelity quantile regression method, whose key innovation lies in a local quantile linking mechanism that expresses high-fidelity quantiles as evaluations of low-fidelity quantiles at covariate-dependent quantile levels. This reformulation transforms the original problem into the estimation of a smoother quantile-level function, complemented by a correction step to enhance robustness. Theoretical analysis demonstrates that, under relatively mild conditions, the proposed approach outperforms baselines that rely solely on high-fidelity data. Empirical results on both synthetic and real-world datasets confirm its ability to yield more accurate quantile estimates and tighter conformal prediction intervals.

Abstract

High-fidelity (HF) data are often expensive to collect and therefore scarce, making conditional quantiles difficult to estimate accurately. We propose a two-stage, model-agnostic method for multi-fidelity quantile regression. The central idea is a local quantile link: at each covariate value, the HF quantile is represented as a low-fidelity (LF) quantile evaluated at a covariate-dependent level. This reformulation reduces the problem to estimating the level function, which can be smoother than the HF quantile itself when the LF and HF conditional distributions have similar shapes. We also study the complementary regime in which this advantage weakens and introduce a correction step to improve robustness. Our theory characterizes when the proposed estimator converges faster than direct quantile regression using HF data alone and when the correction step provides further improvement. Experiments on synthetic and real data show that our method yields more accurate quantile estimates and tighter conformal prediction intervals.

Problem

• multi-fidelity
• quantile regression
• high-fidelity data
• conditional quantiles
• data scarcity

Innovation

• multi-fidelity learning
• quantile regression
• local quantile link
• conformal prediction
• level function estimation