论文标题
多响应中的可解释性学习回归回归
Scalable Interpretable Learning for Multi-Response Error-in-Variables Regression
论文作者
论文摘要
在经济学，金融和生物信息学等各种当代应用中，包含嘈杂或缺失观察结果的损坏的数据集普遍存在。尽管在高维多响应回归中最近的方法论和算法进步，但如何在受污染的协变量下实现可扩展和可解释的估计值。在本文中，我们开发了一种新方法，称为凸条件顺序稀疏学习（COSS），用于在添加测量误差和随机丢失数据下的多种反应回归。它结合了最近开发的顺序稀疏因子回归的强度和最接近的半明确基质投影，从而在大规模关联分析中享有逐步的凸度和可伸缩性。提供了全面的理论保证，我们通过数值研究证明了所提出的方法的有效性。
Corrupted data sets containing noisy or missing observations are prevalent in various contemporary applications such as economics, finance and bioinformatics. Despite the recent methodological and algorithmic advances in high-dimensional multi-response regression, how to achieve scalable and interpretable estimation under contaminated covariates is unclear. In this paper, we develop a new methodology called convex conditioned sequential sparse learning (COSS) for error-in-variables multi-response regression under both additive measurement errors and random missing data. It combines the strengths of the recently developed sequential sparse factor regression and the nearest positive semi-definite matrix projection, thus enjoying stepwise convexity and scalability in large-scale association analyses. Comprehensive theoretical guarantees are provided and we demonstrate the effectiveness of the proposed methodology through numerical studies.
