针对高维强噪声数据，提出两种自适应采样方法，显著提升回归稳定性与精度。
Adaptive and Stratified Subsampling for High-Dimensional Robust Estimation
- 采用自适应重要性采样与分层采样策略，应对重尾噪声和数据依赖问题。
- 在20%污染下误差比均匀采样低3.1倍，Riboflavin数据集测试MSE降低29.5%。
- 适用于高维金融、基因组等存在异常值和时间依赖的数据分析场景。
我们研究在有限方差重尾噪声、epsilon-污染及alpha-混合依赖条件下，基于自适应重要性采样（AIS）和分层采样（SS）的鲁棒高维稀疏回归。在精确界定的子高斯设计与有限方差噪声下，采样规模m可达到极小最大最优率。理论闭环：定理4.6适用于终止时权重稳定的AIS（命题4.1），而SS符合Lecue与Lerasle的中位数均值M-估计框架（命题4.3）。通过新的稀疏精度假设下的节点Lasso精度估计器完成去偏化，实现坐标层面的有效置信区间（定理4.14）。alpha-混合扩展采用日历块协议以保障时间分离（定理4.12）。实验表明，在20%污染下，AIS误差仅为均匀采样的3.10倍；在Riboflavin数据集（p=4,088，n=71）上测试MSE降低29.5%。
原文摘要 · Abstract (English)
We study robust high-dimensional sparse regression under finite-variance heavy-tailed noise, epsilon-contamination, and alpha-mixing dependence via two subsampling estimators: Adaptive Importance Sampling (AIS) and Stratified Sub-sampling (SS). Under sub-Gaussian design whose scopeis precisely delimited and finite-variance noise, a subsample of size m achieves the minimax-optimal rate. We close the theory-algorithm gap: Theorem 4.6 applies to AIS at termination conditional on stabilized weights (Proposition 4.1), and SS fits the median-of-means M-estimation framework of Lecue and Lerasle (Proposition 4.3). The de-biasing step is fully specified via the nodewise-Lasso precision estimator under a new sparse-precision assumption, yielding valid coordinate-wise CIs (Theorem 4.14). The alpha-mixing extension uses a calendar-time block protocol that guarantees temporal separation (Theorem 4.12). Empirically, AIS achieves 3.10 times lower error than uniform subsampling at 20% contamination, and 29.5% lower test MSE on Riboflavin (p=4,088 and n=71).
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