Multi-Fidelity Quantile Regression Method Proposed to Improve Estimation with Limited High-Fidelity Data
A team of researchers has introduced a two-stage, model-agnostic method called multi-fidelity quantile regression that leverages abundant low-fidelity data to improve estimates when high-fidelity data is expensive and scarce. The approach uses a 'local quantile link' to express high-fidelity quantiles in terms of low-fidelity quantiles at a covariate-dependent level, reducing the estimation problem to a potentially smoother function. The method could benefit applications in science and engineering where collecting high-quality observations is costly, while also producing tighter conformal prediction intervals.
Researchers have posted a preprint on arXiv presenting a two-stage, model-agnostic framework for multi-fidelity quantile regression, targeting settings where high-fidelity (HF) data are too expensive to collect in large quantities. The core innovation is a 'local quantile link': at each covariate value, the HF conditional quantile is re-expressed as a low-fidelity (LF) quantile evaluated at a learned, covariate-dependent probability level. This reformulation can be advantageous when the LF and HF conditional distributions share similar shapes, because the level function to be estimated may be smoother than the HF quantile itself. The authors also analyze a complementary regime where this smoothness advantage weakens and introduce a correction step designed to improve robustness in those cases. Theoretical results characterize conditions under which the proposed estimator converges faster than direct quantile regression on HF data alone, and when the correction step yields additional gains. Experiments on both synthetic and real datasets demonstrate improved quantile accuracy and tighter conformal prediction intervals compared to baselines. The paper, spanning 69 pages with 12 figures and 3 tables, was submitted in May 2026 and revised in June 2026.
What's missing
As a preprint, this work has not yet undergone formal peer review, so the theoretical claims and experimental results have not been independently validated. The real-data domains used in experiments are not described in the abstract, limiting assessment of practical scope.
What different sources said
- arXiv stat.MLCenter
Multi-Fidelity Quantile Regression
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