存在测量误差的高斯图模型估计  

Gaussian graphical model estimation with measurement error

作　　者：王向禄 Xianglu Wang(Department of Statistics and Finance,School of Management,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学管理学院统计与金融系,安徽合肥230026

出　　处：《中国科学技术大学学报》2023年第11期42-52,I0005,I0008,共13页JUSTC

摘　　要：众所周知,如果将损坏的数据直接应用于为干净数据设计的回归方法中,将导致错误的结果。尽管最近高斯图模型估计在方法以及算法上都取得了不错的进展,但如何在受污染的协变量下实现高效和可扩展的高斯图模型估计尚不清楚。本文针对加性和乘性测量误差下的高斯图模型开发了一种称为凸条件创新可扩展有效估计(COCOISEE)的新方法。该方法结合了高斯图模型中创新的可扩展高效估计和最近半正定矩阵投影的优点,从而在估计过程中具有逐步凸性和可扩展性。我们为该方法提供了全面的理论保证,并且通过数值研究证明了所提出方法的有效性。It is well known that regression methods designed for clean data will lead to erroneous results if directly applied to corrupted data.Despite the recent methodological and algorithmic advances in Gaussian graphical model estimation,how to achieve efficient and scalable estimation under contaminated covariates is unclear.Here a new methodology called convex conditioned innovative scalable efficient estimation(COCOISEE)for Gaussian graphical models under both additive and multiplicative measurement errors is developed.It combines the strengths of the innovative scalable efficient estimation in the Gaussian graphical model and the nearest positive semidefinite matrix projection,thus enjoying stepwise convexity and scalability.Comprehensive theoretical guarantees are provided and the effectiveness of the proposed methodology is demonstrated through numerical studies.

关 键 词：高斯图模型 测量误差 可扩展性 逐步凸性 

分 类 号：O212.4[理学—概率论与数理统计]