2024/10/16 by Prateek Mittal, Mittal, Prateek, Joohi Chauhan +2
Computer Science · Engineering · #Anomaly Detection Techniques and Applications #FOS: Computer and information sciences #FOS: Mathematics #Image Processing Techniques and Applications #Machine Learning (cs.LG) #Machine Learning and Algorithms #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2410.12367
openalex publication_date 2024/10/16 · openalex created_date 2024/10/20 · openalex updated_date 2026/07/28
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).