2016/08/12 by Mohammad Taha Bahadori, Zemin Zheng, Bahadori, Mohammad Taha +5
Computer Science · Engineering · Mathematics · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #stat.ME
paper · pdf · doi:10.48550/arxiv.1608.03686
31 pages, 7 figures
arxiv created 2016/08/12 · openalex publication_date 2016/08/12 · arxiv updated 2016/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Sparse reduced-rank regression is an important tool to uncover meaningful dependence structure between large numbers of predictors and responses in many big data applications such as genome-wide association studies and social media analysis. Despite the recent theoretical and algorithmic advances, scalable estimation of sparse reduced-rank regression remains largely unexplored. In this paper, we suggest a scalable procedure called sequential estimation with eigen-decomposition (SEED) which needs only a single top-r singular value decomposition to find the optimal low-rank and sparse matrix by solving a sparse generalized eigenvalue problem. Our suggested method is not only scalable but also performs simultaneous dimensionality reduction and variable selection. Under some mild regularity conditions, we show that SEED enjoys nice sampling properties including consistency in estimation, rank selection, prediction, and model selection. Numerical studies on synthetic and real data sets show that SEED outperforms the state-of-the-art approaches for large-scale matrix estimation problem.