Heterogeneity-calibrated Byzantine-robust distributed composite quantile regression
Abstract
We study sparse composite quantile regression (CQR) for distributed data with heterogeneous honest sites and Byzantine workers. Honest sites share a common slope but may differ in their covariate distributions, error laws, and quantile intercepts. The proposed heterogeneity-calibrated robust CQR (HC-RCQR) profiles local intercepts and calibrates scores using an approximate inverse profile Hessian. Honest workers transmit the resulting vectors, whereas Byzantine workers may send arbitrary vectors. The server updates the estimate by coordinatewise trimming and soft thresholding. A scalar example shows how unequal honest-site curvatures allow intermediate Byzantine reports to survive trimming and how ideal calibration reduces their possible effect. We also establish nonidentification of the mean of unrestricted honest-site slopes when fault identities are unknown. Under suitable conditions, we establish conditional contraction and support-recovery guarantees. The bound separates score offset, sampling fluctuation, contamination, calibration error, and the Newton remainder. Simulations and a bike-demand study examine performance under heterogeneous data and adversarial messages.
Related
- Byzantine-Robust Sparse Regression with Missing Covariates
- Byzantine-tolerant distributed learning of finite mixture models under partial corruptions
- Max-Test-Calibrated Stein Shrinkage with Honest Submodel Selection in Ultra-High-Dimensional Regression
- Distributed Selective Inference for Quantile Regression
- Asymptotic Risk of Learning-Rate Schedules for Least-Squares Regression with Discretely Distributed Features
BibTeX
@misc{wu2026heterogeneitycalibrated,
title = {{Heterogeneity-calibrated Byzantine-robust distributed composite quantile regression}},
author = {Xiaofei Wu and Jian Qing Shi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19701},
eprint = {2609.19701},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19701},
}
RIS
TY - UNPB
TI - Heterogeneity-calibrated Byzantine-robust distributed composite quantile regression
AU - Xiaofei Wu
AU - Jian Qing Shi
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19701
UR - https://arxiv.org/abs/2609.19701
AB - We study sparse composite quantile regression (CQR) for distributed data with heterogeneous honest sites and Byzantine workers. Honest sites share a common slope but may differ in their covariate distributions, error laws, and quantile intercepts. The proposed heterogeneity-calibrated robust CQR (HC-RCQR) profiles local intercepts and calibrates scores using an approximate inverse profile Hessian. Honest workers transmit the resulting vectors, whereas Byzantine workers may send arbitrary vectors. The server updates the estimate by coordinatewise trimming and soft thresholding. A scalar example shows how unequal honest-site curvatures allow intermediate Byzantine reports to survive trimming and how ideal calibration reduces their possible effect. We also establish nonidentification of the mean of unrestricted honest-site slopes when fault identities are unknown. Under suitable conditions, we establish conditional contraction and support-recovery guarantees. The bound separates score offset, sampling fluctuation, contamination, calibration error, and the Newton remainder. Simulations and a bike-demand study examine performance under heterogeneous data and adversarial messages.
ER -