发表机构
Yunnan Key Laboratory of Statistical Modeling and Data Analysis, School of Mathematics and Statistics, Yunnan University; Department of Statistics and Data Science, Beijing Normal–Hong Kong Baptist University（云南大学数学与统计学院; 北京师范大学-香港浸会大学联合国际学院统计与数据科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对异质性诚实站点与拜占庭工作节点，提出异质性校准鲁棒复合分位数回归方法，通过剖面校准与坐标修剪实现鲁棒估计，并提供理论保证与实验验证。
AI 中文摘要
我们研究了针对具有异质性诚实站点和拜占庭工作节点的分布式数据的稀疏复合分位数回归（CQR）。诚实站点共享共同的斜率，但其协变量分布、误差法则和分位数截距可能不同。所提出的异质性校准鲁棒CQR（HC-RCQR）方法通过近似逆剖面Hessian矩阵对局部截距进行剖面化处理并校准分数。诚实工作节点传输由此得到的向量，而拜占庭工作节点可能发送任意向量。服务器通过坐标修剪和软阈值化更新估计。一个标量示例展示了不相等的诚实站点曲率如何使中间拜占庭报告在修剪中幸存，以及理想校准如何减少其可能的影响。我们还证明了在故障身份未知时，无限制诚实站点斜率均值的不可识别性。在适当条件下，我们建立了条件收缩和支持恢复保证。该界限分离了分数偏移、采样波动、污染、校准误差和牛顿余项。模拟实验和一项自行车需求研究检验了在异质性数据和对抗性消息下的性能。
英文摘要
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.
