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Convex formulation for regularized estimation of structural equation models

机译：用于结构方程模型正则估计的凸公式

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摘要

Path analysis is a model class of structural equation modeling (SEM), which it describes causal relations among measured variables in the form of a multiple linear regression. This paper presents two estimation formulations, one each for confirmatory and exploratory SEM, where a zero pattern of the estimated path matrix can explain a causality structure of the variables. The original nonlinear equality constraints of the model parameters were relaxed to an inequality, allowing the transformation of the original problem into a convex framework. A regularized estimation formulation was then proposed for exploratory SEM using an 11-type penalty of the path coefficient matrix. Under a condition on problem parameters, our optimal solution is low rank and provides a useful solution to the original problem. Proximal algorithms were applied to solve our convex programs in a large-scale setting. The performance of this approach was demonstrated in both simulated and real data sets, and in comparison with an existing method. When applied to two real applications (learning causality among climate variables and examining brain connectivity in autism patients using fMRI time series from ABIDE data set) the findings could explain known relationships among environmental variables and discern known and new brain connectivity differences, respectively. (C) 2019 Elsevier B.V. All rights reserved.
机译：路径分析是结构方程模型（SEM）的模型类，它以多元线性回归的形式描述测量变量之间的因果关系。本文提出了两种估计公式，分别用于验证性和探索性SEM，其中估计路径矩阵的零模式可以解释变量的因果结构。将模型参数的原始非线性等式约束放宽为不等式，从而可以将原始问题转换为凸框架。然后，使用路径系数矩阵的11型罚分提出了用于探索性SEM的正则估计公式。在有问题参数的条件下，我们的最优解是低秩的，它为原始问题提供了有用的解决方案。应用近邻算法来大规模解决我们的凸程序。在模拟数据集和实际数据集中，以及与现有方法相比，都证明了这种方法的性能。当应用于两个实际应用（学习气候变量之间的因果关系，并使用来自ABIDE数据集的fMRI时间序列来检查自闭症患者的大脑连通性）时，这些发现可以解释环境变量之间的已知关系，并分别识别已知和新的大脑连通性差异。 （C）2019 Elsevier B.V.保留所有权利。

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