发表机构
The University of Texas at Austin; Florida State University; Texas A&M University（德克萨斯大学奥斯汀分校; 佛罗里达州立大学; 德州农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非高斯误差的结构方程模型，提出基于分数的DAG学习方法MARCEDES，通过连续优化与稀疏惩罚实现高效因果发现，模拟实验验证其优于现有方法。
AI 中文摘要
我们考虑学习对应于具有非高斯误差的结构方程模型（SEM）的潜在因果有向无环图（DAG）结构的问题。受一个故意错误设定的、所有误差均为拉普拉斯分布的非高斯SEM的启发，我们首先引入定义在所有实矩阵空间上的平均绝对残差风险，并证明在渐近意义上，真实加权因果DAG矩阵的风险严格小于任何其他矩阵的风险。然而，为了增强通用性并适应高维和有限样本场景，我们进一步结合行特定的稀疏惩罚以及一个软DAG约束，推导出定义在实矩阵空间上的连续分数函数。据此，我们提出了一种名为MARCEDES的基于分数的DAG学习方法，将其表述为一个无约束的分数最小化问题，该问题可以使用基于梯度的优化技术高效求解，从而规避了约束优化带来的挑战。此外，我们开发了一种计算算法来处理分数目标的非光滑性，并在广义贝叶斯框架下实现行特定稀疏惩罚的最优调整。最后，我们通过广泛的模拟研究证明了所提出方法相对于现有方法的效率和改进的性能。
英文摘要
We consider the problem of learning the underlying causal directed acyclic graph (DAG) structure corresponding to a structural equation model (SEM) with non-Gaussian errors. Motivated by an intentionally misspecified non-Gaussian SEM with all Laplace errors, we first introduce the mean absolute residual risk, defined over the space of all real matrices, and show that, asymptotically, the risk of the true weighted causal DAG matrix is strictly smaller than that of any other matrix. Nevertheless, to enhance generality and account for high-dimensional and finite-sample settings, we further incorporate row-specific sparsity penalties along with a soft DAG constraint to derive a continuous score function over the space of real matrices. Accordingly, we propose a score-based DAG learning method, named MARCEDES, formulated as an unconstrained score minimization problem, which can be efficiently solved using gradient-based optimization techniques, thereby circumventing the challenges associated with constrained optimization. Furthermore, we develop a computational algorithm to handle the non-smoothness of the score objective and to enable optimal tuning of row-specific sparsity penalties under a generalized Bayes framework. Finally, we demonstrate the efficiency and improved performance of the proposed method over existing approaches through an extensive simulation study.
