Multi-Fidelity Quantile Regression

TL;DR

This paper introduces a two-stage, model-agnostic multi-fidelity quantile regression method that leverages low-fidelity data to improve high-fidelity quantile estimation, with theoretical and empirical validation.

Contribution

It proposes a novel local quantile link approach and a correction step, enhancing quantile estimation accuracy using multi-fidelity data compared to existing methods.

Findings

The method converges faster than direct HF quantile regression under certain conditions.

The correction step improves robustness when the local quantile link advantage weakens.

Experiments show 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.