通过联合回归估计高维稀疏逆协方差与偏相关矩阵
Inverse Covariance and Partial Correlation Matrix Estimation via Joint Partial Regression
- 利用回归关系建模逆协方差结构，分两阶段实现
- 理论给出非渐近估计误差上界，证明方法可靠性
- 适合高维数据中变量依赖关系建模，如基因组分析
本文提出一种估计稀疏高维逆协方差矩阵和偏相关矩阵的方法，利用逆协方差矩阵与线性回归之间的联系。该方法为两阶段估计：每个特征对其他所有特征进行回归，同时强制保证半正定性。我们推导了逆协方差矩阵和偏相关矩阵估计的非渐近误差率。此外，还提出了一个高效的近端分裂算法用于数值计算。在合成数据和真实数据上的实验验证了该方法的有效性。
原文摘要 · Abstract (English)
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation method wherein each individual feature is regressed on all other features while positive semi-definiteness is enforced simultaneously. We derive non-asymptotic estimation rates for both inverse covariance and partial correlation matrix estimation. An efficient proximal splitting algorithm for numerically computing the estimate is also dervied. The effectiveness of the proposed method is demonstrated on both synthetic and real-world data.
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