Sparse permutation invariant covariance estimation
Sparse permutation invariant covariance estimation
复制标题
DOI：
10.1214/08-ejs176
复制
发表时间：
2008-01-01
影响因子：
1.1
通讯作者：
Zhu, Ji
中科院分区：
文献类型：
--
作者：
Rothman, Adam J.;Bickel, Peter J.;Zhu, Ji
本文提出了一种在高维环境下构建逆协方差（浓度）矩阵的稀疏估计量的方法。该估计量采用惩罚化的正态似然方法，并通过使用套索型惩罚来强制稀疏性。当数据维度\(p\)和样本量\(n\)都允许增长时，我们确定了弗罗贝尼乌斯范数下的收敛速度，并表明该速度明确取决于真实浓度矩阵的稀疏程度。我们还表明，该方法的基于相关性的版本在算子范数下表现出更好的速度。我们还推导了一种用于计算估计量的快速迭代算法，该算法依赖于逆矩阵的常用乔列斯基分解，但产生一个置换不变估计量。在模拟数据以及使用基因表达数据对肿瘤组织分类的一个实际数据示例上，将该方法与其他估计量进行了比较。
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. We establish a rate of convergence in the Frobenius norm as both data dimension p and sample size n are allowed to grow, and show that the rate depends explicitly on how sparse the true concentration matrix is. We also show that a correlation-based version of the method exhibits better rates in the operator norm. We also derive a fast iterative algorithm for computing the estimator, which relies on the popular Cholesky decomposition of the inverse but produces a permutation-invariant estimator. The method is compared to other estimators on simulated data and on a real data example of tumor tissue classification using gene expression data.