通过SURE调优的岭回归实现等方差线性高斯有向无环图的因果发现
Causal Discovery in Equal Variance Linear Gaussian DAGs via SURE-Tuned Ridge Regression
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中文总结 AI 辅助
针对因果发现中连续优化方法难以适配样本有限、计算有限场景的问题，提出SURE-Ridge方法，在小样本下结构汉明距离最低且所有样本量下运行时间最短。
中文摘要 AI 辅助
从观测数据中恢复结构方程模型（SEM）的有向无环图（DAG）是因果发现的核心问题。连续优化方法的迭代梯度下降和针对每个问题的超参数调优，难以适配两类实际重要场景：样本有限场景（样本数量与DAG节点数量相当或更少）和计算有限场景。本研究提出SURE-Ridge，一种针对等方差线性高斯SEM的非迭代闭式估计器。该方法执行并行节点回归，正则化参数由斯坦无偏风险估计（SURE）自适应选择，并应用自适应阈值处理从得到的软邻接矩阵中提取DAG。数值结果表明，与NOTEARS、DAGMA和GBNSL基线相比，SURE-Ridge在小样本场景下实现了最低的结构汉明距离，且在所有测试样本量下运行时间最短。
英文摘要
Recovering the directed acyclic graph (DAG) of a structural equation model (SEM) from observational data is a central problem in causal discovery. The iterative gradient descent and per-problem hyperparameter tuning of continuous-optimization methods are poorly suited to two practically important regimes: the sample-limited regime, where the number of samples is comparable to or smaller than the number of nodes in the DAG, and the compute-limited regime. This work proposes SURE-Ridge, a non-iterative, closed-form estimator for equal variance linear Gaussian SEM. The method performs parallel node-wise regressions with regularization parameters chosen adaptively by Stein's unbiased risk estimate (SURE), and applies an adaptive thresholding procedure to extract a DAG from the resulting soft adjacency matrix. Numerical results show that SURE-Ridge achieves the lowest structural Hamming distance in the small-sample regime and the lowest run time across all sample sizes tested, compared with NOTEARS, DAGMA, and GBNSL baselines.
发表机构
- University of Southern California（南加州大学）
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