A proximal distance algorithm for likelihood-based sparse covariance estimation.

IF 2.4 2区 数学 Q2 BIOLOGY
Biometrika Pub Date : 2022-12-01 Epub Date: 2022-02-16 DOI:10.1093/biomet/asac011
Jason Xu, Kenneth Lange
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引用次数: 2

Abstract

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.

基于似然法的稀疏协方差估计的近距离算法。
本文探讨了在无模式稀疏性假设下估计协方差矩阵的任务。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法的方法,该方法对协方差估计到对称稀疏集的距离进行正则化处理。这种方法避免了更常见的规范惩罚所引起的不必要的收缩,并通过解决一系列平滑、无约束的子问题来优化由此产生的非凸目标。这些子问题是通过大化-最小化原理的近距离版本生成和求解的。由此产生的算法执行迅速,能从容应对参数数量超过案例数量的情况,产生正有限解,并具有理想的收敛特性。经验表明,在一系列模拟实验中,我们的方法在多个指标上都优于其他竞争方法。我们通过国际移民数据和流式细胞仪案例研究说明了这种方法的优点。我们的研究结果表明,细胞信号数据的边际依赖网络和条件依赖网络比以前得出的结论更为相似。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Biometrika
Biometrika 生物-生物学
CiteScore
5.50
自引率
3.70%
发文量
56
审稿时长
6-12 weeks
期刊介绍: Biometrika is primarily a journal of statistics in which emphasis is placed on papers containing original theoretical contributions of direct or potential value in applications. From time to time, papers in bordering fields are also published.
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