TY - GEN
T1 - Differentially Private Quantile Regression
AU - Tran, Tran
AU - Reimherr, Matthew Logan
AU - Slavkovic, Aleksandra
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - Quantile regression (QR) is a powerful and robust statistical modeling method broadly used in many fields such as economics, ecology, and healthcare. However, it has not been well-explored in differential privacy (DP) since its loss function lacks strong convexity and twice differentiability, often required by many DP mechanisms. We implement the smoothed QR loss via convolution within the K-Norm Gradient mechanism (KNG) and prove the resulting estimate converges to the non-private one asymptotically. Additionally, our work is the first to extensively investigate the empirical performance of DP smoothing QR under pure-, approximate- and concentrated-DP and four mechanisms, and cases commonly encountered in practice such as heavy-tailed and heteroscedastic data. We find that the Objective Perturbation Mechanism and KNG are the top performers across the simulated settings.
AB - Quantile regression (QR) is a powerful and robust statistical modeling method broadly used in many fields such as economics, ecology, and healthcare. However, it has not been well-explored in differential privacy (DP) since its loss function lacks strong convexity and twice differentiability, often required by many DP mechanisms. We implement the smoothed QR loss via convolution within the K-Norm Gradient mechanism (KNG) and prove the resulting estimate converges to the non-private one asymptotically. Additionally, our work is the first to extensively investigate the empirical performance of DP smoothing QR under pure-, approximate- and concentrated-DP and four mechanisms, and cases commonly encountered in practice such as heavy-tailed and heteroscedastic data. We find that the Objective Perturbation Mechanism and KNG are the top performers across the simulated settings.
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U2 - 10.1007/978-3-031-69651-0_2
DO - 10.1007/978-3-031-69651-0_2
M3 - Conference contribution
AN - SCOPUS:85205123850
SN - 9783031696503
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 18
EP - 34
BT - Privacy in Statistical Databases - International Conference, PSD 2024, Proceedings
A2 - Domingo-Ferrer, Josep
A2 - Önen, Melek
PB - Springer Science and Business Media Deutschland GmbH
T2 - International Conference on Privacy in Statistical Databases, PSD 2024
Y2 - 25 September 2024 through 27 September 2024
ER -