A proximal distance algorithm for likelihood-based sparse covariance estimation.
A proximal distance algorithm for likelihood-based sparse covariance estimation.
复制标题
用于基于似然的稀疏协方差估计的近端距离算法。
DOI：
10.1093/biomet/asac011
复制
发表时间：
2022
期刊：
影响因子：
2.7
通讯作者：
Lange,Kenneth
中科院分区：
文献类型：
--
作者：
Xu,Jason;Lange,Kenneth
本文讨论了在无模式稀疏假设下估计协方差矩阵的问题。与现有的基于阈值或收缩惩罚的方法不同，我们提出了一种基于似然的方法，该方法将协方差估计到对称稀疏集的距离正则化。该公式避免了由更常见的范数惩罚引起的不必要的收缩，并通过求解一系列光滑的、无约束子问题来优化所产生的非凸目标。这些子问题是通过最优-最小化原理的最近距离版本产生和求解的。所得到的算法执行迅速，优雅地处理参数数量超过案例数量的设置，产生正定解，并具有理想的收敛特性。从经验上看，我们的方法在几个指标上都优于竞争对手的方法，并进行了一系列模拟实验。它的优点在国际迁移数据和流式细胞术的案例研究中得到了说明。我们的发现表明，细胞信令数据的边际和条件依赖网络比之前得出的结论更相似。
This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes the distance from the covariance estimate to a symmetric sparsity set. This formulation avoids unwanted shrinkage induced by more common norm penalties, and enables optimization of the resulting nonconvex objective by solving a sequence of smooth, unconstrained subproblems. These subproblems are generated and solved via the proximal distance version of the majorization-minimization principle. The resulting algorithm executes rapidly, gracefully handles settings where the number of parameters exceeds the number of cases, yields a positive-definite solution, and enjoys desirable convergence properties. Empirically, we demonstrate that our approach outperforms competing methods across several metrics, for a suite of simulated experiments. Its merits are illustrated on international migration data and a case study on flow cytometry. Our findings suggest that the marginal and conditional dependency networks for the cell signalling data are more similar than previously concluded.