Causal Discovery in Equal Variance Linear Gaussian DAGs via SURE-Tuned Ridge Regression

• URL: http://arxiv.org/abs/2608.17132v1
• Date: Mon, 17 Aug 2026 21:07:06 GMT
• Title: Causal Discovery in Equal Variance Linear Gaussian DAGs via SURE-Tuned Ridge Regression
• Abstract summary: SURE-Ridge is a non-iterative, closed-form estimator for equal variance linear Gaussian SEM.<n>It achieves the lowest structural Hamming distance in the small-sample regime and the lowest run time across all sample sizes tested.
• Score: 18.884190660925444
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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