ON CONSISTENCY AND SPARSITY FOR SLICED INVERSE REGRESSION IN HIGH DIMENSIONS
ON CONSISTENCY AND SPARSITY FOR SLICED INVERSE REGRESSION IN HIGH DIMENSIONS
复制标题
DOI：
10.1214/17-aos1561
复制
发表时间：
2018-04-01
影响因子：
4.5
通讯作者：
Liu, Jun S.
中科院分区：
文献类型：
--
作者：
Lin, Qian;Zhao, Zhigen;Liu, Jun S.
这里我们提供了一个框架来分析切片逆回归(SIR)的相变现象，SIR是Li[J.Amer]提出的一种有监督的降维技术。统计学家。阿索克。86(1991)316-342]。在较温和的条件下，渐近比Rho=Limp/n是相变参数，且SIR估计量相容的充要条件是Rho=0。当维度p大于n时，我们提出了对角阈值筛选SIR(DT-SIR)算法。该方法给出了条件期望的协方差矩阵var(E[x垂直条形y])的特征空间的估计。然后，通过将协方差矩阵的逆乘在特征空间上来获得期望的降维空间。在预报器协方差矩阵和方向载荷均满足一定的稀疏性假设下，证明了DT-SIR在高维数据分析中估计降维空间的一致性。大量的数值实验表明，与竞争对手相比，该方法具有更好的性能。
We provide here a framework to analyze the phase transition phenomenon of slice inverse regression (SIR), a supervised dimension reduction technique introduced by Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]. Under mild conditions, the asymptotic ratio rho = lim p/n is the phase transition parameter and the SIR estimator is consistent if and only if rho = 0. When dimension p is greater than n, we propose a diagonal thresholding screening SIR (DT-SIR) algorithm. This method provides us with an estimate of the eigenspace of var(E [x vertical bar y]), the covariance matrix of the conditional expectation. The desired dimension reduction space is then obtained by multiplying the inverse of the covariance matrix on the eigenspace. Under certain sparsity assumptions on both the covariance matrix of predictors and the loadings of the directions, we prove the consistency of DT-SIR in estimating the dimension reduction space in high-dimensional data analysis. Extensive numerical experiments demonstrate superior performances of the proposed method in comparison to its competitors.