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

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.

5 Pages, 3 Figures. Accepted at 60th Asilomar Conference on Signals, Systems, and Computers 2026

Machine Learning (cs.LG); Signal Processing (eess.SP); Machine Learning (stat.ML)

arXiv:2608.17132 [cs.LG]

(or arXiv:2608.17132v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.17132 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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