提出无需迭代的快速因果图推断方法，小样本下更准更快。
Causal Discovery in Equal Variance Linear Gaussian DAGs via SURE-Tuned Ridge Regression
- 用SURE自适应选正则化参数，闭式解一步到位
- 小样本下结构哈明距离最低，全量级运行最快
- 适合数据少或算力有限的因果推断场景
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。连续优化方法依赖迭代梯度下降和逐问题调参，在样本受限（样本数接近或小于节点数）和计算受限场景下表现不佳。本文提出SURE-Ridge，一种针对等方差线性高斯SEM的非迭代、闭式估计器。该方法通过并行节点回归，以斯坦因无偏风险估计（SURE）自适应选择正则化参数，并采用自适应阈值法从软邻接矩阵中提取DAG。数值实验表明，相比NOTEARS、DAGMA和GBNSL基线，SURE-Ridge在小样本条件下实现最低的结构哈明距离，且在所有测试样本规模下运行时间最短。
原文摘要 · Abstract (English)
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.
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