Multi-Fidelity Quantile Regression Method Proposed to Improve Estimation with Limited High-Fidelity Data
Researchers propose a two-stage method for quantile regression that leverages both expensive high-fidelity and cheaper low-fidelity data to improve conditional quantile estimation. The approach uses a local quantile link that represents high-fidelity quantiles through low-fidelity quantiles at covariate-dependent levels, reducing the estimation problem to a potentially smoother function. The method is significant because it addresses the practical challenge of scarce high-fidelity data in machine learning applications while providing theoretical guarantees and empirical improvements in prediction accuracy.
A new model-agnostic approach to multi-fidelity quantile regression has been introduced to address the challenge of estimating accurate conditional quantiles when high-fidelity data are expensive and limited. The method employs a two-stage process centered on a local quantile link, where high-fidelity quantiles are expressed as low-fidelity quantiles evaluated at covariate-dependent levels. This reformulation transforms the problem into estimating a level function, which can be smoother and easier to estimate than the high-fidelity quantile directly when the conditional distributions of low-fidelity and high-fidelity data share similar shapes. The authors provide theoretical analysis characterizing convergence rates and conditions under which the method outperforms direct quantile regression using only high-fidelity data, and introduce a correction step for improved robustness in complementary regimes. Experiments on both synthetic and real datasets demonstrate that the approach produces more accurate quantile estimates and tighter conformal prediction intervals.
What's missing
The paper does not discuss computational complexity or scalability of the proposed method, nor does it provide guidance on practical implementation details such as hyperparameter selection or software availability. Additionally, the specific real-world datasets used in experiments are not detailed in the abstract, limiting reproducibility assessment.
What different sources said
- arXiv stat.MLCenter
Multi-Fidelity Quantile Regression
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