We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present sharper error bounds under weaker assumptions than prior studies that share similar interests with this study. Our analysis relies on some sharp concentration inequalities resulting from generic chaining.

翻译：本文研究线性回归系数的离群点鲁棒与稀疏估计问题，其中协变量与噪声均受到对抗性离群点污染，且噪声采样自重尾分布。相较于具有相似研究目标的前期工作，本文在更弱的假设条件下给出了更尖锐的误差界。我们的分析依赖于通过泛化链式方法导出的若干尖锐集中不等式。