With the ubiquity of personal‑level data collection, protecting individual privacy has become a critical concern in statistical modeling. This paper proposes Diff‑QR, a Differential‑Privacy Quantile Regression framework that achieves accurate conditional quantile estimation while rigorously preserving privacy. Diff‑QR decomposes the quantile regression objective into two sub‑functions whose global sensitivities are analytically derived. An adaptive privacy‑budget allocation scheme, proportional to the sensitivity ratio, injects Laplace noise into each sub‑function, thus reducing the overall perturbation required for a given privacy level ε. We formally prove that Diff‑QR satisfies ε‑differential privacy and analyze its error bounds. Extensive Monte Carlo studies and two real‑world cases (spectroscopy signal calibration and blueberry yield prediction) show that Diff‑QR attains lower and more stable mean‑squared error (MSE) than naïve noise‑randomized quantile regression across a wide range of ε and quantile levels τ. The method offers a practical route to privacy‑preserving regression analysis in large‑scale data environments.

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Differential Privacy Budget Allocation for Quantile Regression Analysis

  • Dongfeng Zhu

摘要

With the ubiquity of personal‑level data collection, protecting individual privacy has become a critical concern in statistical modeling. This paper proposes Diff‑QR, a Differential‑Privacy Quantile Regression framework that achieves accurate conditional quantile estimation while rigorously preserving privacy. Diff‑QR decomposes the quantile regression objective into two sub‑functions whose global sensitivities are analytically derived. An adaptive privacy‑budget allocation scheme, proportional to the sensitivity ratio, injects Laplace noise into each sub‑function, thus reducing the overall perturbation required for a given privacy level ε. We formally prove that Diff‑QR satisfies ε‑differential privacy and analyze its error bounds. Extensive Monte Carlo studies and two real‑world cases (spectroscopy signal calibration and blueberry yield prediction) show that Diff‑QR attains lower and more stable mean‑squared error (MSE) than naïve noise‑randomized quantile regression across a wide range of ε and quantile levels τ. The method offers a practical route to privacy‑preserving regression analysis in large‑scale data environments.