In many scientific studies, it becomes increasingly important to delineate the pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate the pathway effects, commonly expressed as the product of coefficients. However, it becomes unstable and computationally challenging to fit such models with high-dimensional mediators. This paper proposes a sparse mediation model using a regularized SEM approach, where sparsity means that a small number of mediators have a nonzero mediation effect between a treatment and an outcome. To address the model selection challenge, we innovate by introducing a new penalty called Pathway Lasso. This penalty function is a convex relaxation of the non-convex product function for the mediation effects, and it enables a computationally tractable optimization criterion to estimate and select pathway effects simultaneously. We develop a fast ADMM-type algorithm to compute the model parameters, and we show that the iterative updates can be expressed in closed form. We also prove the asymptotic consistency of our Pathway Lasso estimator for the mediation effect. On both simulated data and an fMRI data set, the proposed approach yields higher pathway selection accuracy and lower estimation bias than competing methods.

中文翻译：

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Pathway Lasso：高维中介的路径估计和选择


在许多科学研究中，描绘通过大量介质（例如遗传和大脑介质）的途径变得越来越重要。结构方程模型 (SEM) 是一种估计路径效应的流行技术，通常表示为系数的乘积。然而，将此类模型与高维中介进行拟合会变得不稳定且计算上具有挑战性。本文提出了一种使用正则化 SEM 方法的稀疏中介模型，其中稀疏意味着少数中介在治疗和结果之间具有非零中介效应。为了解决模型选择的挑战，我们通过引入一种名为Pathway Lasso的新惩罚进行创新。该惩罚函数是中介效应的非凸乘积函数的凸松弛，并且它使得计算上易于处理的优化标准能够同时估计和选择路径效应。我们开发了一种快速 ADMM 型算法来计算模型参数，并且表明迭代更新可以用封闭形式表示。我们还证明了 Pathway Lasso 估计器对于中介效应的渐近一致性。在模拟数据和功能磁共振成像数据集上，所提出的方法比竞争方法产生更高的路径选择精度和更低的估计偏差。