Byzantine-Robust Sparse Regression with Missing Covariates
Abstract
We study distributed sparse linear regression with missing covariates and Byzantine workers. Correcting for missing observations can make the regression loss nonconvex, while Byzantine reports can distort gradient updates and impair estimation. A communication-efficient method is proposed that combines robust gradient aggregation with folded-concave regularization. Under appropriate regularity conditions, after t communication rounds the estimation error is bounded by a transient component determined by the initial error and decaying geometrically with t, plus a residual component reflecting finite-sample variability and Byzantine contamination. Simulations and two real-data examples evaluate estimation accuracy, variable selection, and communication costs.
Related
- Doubly robust target inference for generalized linear regression with completely missing covariates
- Augmented transfer regression learning for completely missing covariates
- Heterogeneity-calibrated Byzantine-robust distributed composite quantile regression
- Assumption-lean logistic regression with missing covariates
- Sparse Regression Distilled from a Single Robust Fit
BibTeX
@misc{wu2026byzantinerobust,
title = {{Byzantine-Robust Sparse Regression with Missing Covariates}},
author = {Xiaofei Wu and Rongmei Liang and Jian Qing Shi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35321},
eprint = {2610.35321},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35321},
}
RIS
TY - UNPB
TI - Byzantine-Robust Sparse Regression with Missing Covariates
AU - Xiaofei Wu
AU - Rongmei Liang
AU - Jian Qing Shi
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35321
UR - https://arxiv.org/abs/2610.35321
AB - We study distributed sparse linear regression with missing covariates and Byzantine workers. Correcting for missing observations can make the regression loss nonconvex, while Byzantine reports can distort gradient updates and impair estimation. A communication-efficient method is proposed that combines robust gradient aggregation with folded-concave regularization. Under appropriate regularity conditions, after t communication rounds the estimation error is bounded by a transient component determined by the initial error and decaying geometrically with t, plus a residual component reflecting finite-sample variability and Byzantine contamination. Simulations and two real-data examples evaluate estimation accuracy, variable selection, and communication costs.
ER -