用集中不等式证明精度矩阵的收敛速率  

Proving Convergence Rateof Precision Matrix with Centralized Inequality

作　　者：胡芳婷 HU Fang-ting(School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《兰州文理学院学报（自然科学版）》2024年第6期24-30,共7页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：在神经连接模式和社会网络分析等环境中,估计精度矩阵是一个很重要问题.在高维条件下,基于固定维数的经典方法和结果不再适用,稳定准确地估计精度矩阵问题变得尤为重要.为了估计高维精度矩阵,采用了自适应约束l_1范数最小化的精度矩阵估计方法,给出了精度矩阵在一类矩阵范数损失下的收敛速率,并用集中不等式进行详细的证明.In the context of neural connection patterns and social network analysis,estimating precision matrix is an important issue.Under high-dimensional conditions,the classical methods and results based on fixed dimensions are no longer applicable,and the problem of stable and accurate estimation precision matrix becomes particularly important.In order to estimate the high-dimensional precision matrix,this paper adopts the precision matrix estimation method with adaptive constraint l 1 norm minimization,and gives the convergence rate of the precision matrix under the norm loss of a class of matrices,and uses concentration inequalities to prove it in detail.

关 键 词：精度矩阵 集中不等式 收敛速率 

分 类 号：O212[理学—概率论与数理统计]