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

2026-08-17

AI Summary

本文提出SURE-Ridge方法，通过非迭代闭式估计和自适应正则化解决小样本条件下线性高斯DAG模型的因果发现问题。

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.

Problem

• causal discovery
• directed acyclic graph (DAG)
• structural equation model (SEM)
• observational data

Innovation

• SURE-Ridge
• Stein's unbiased risk estimate (SURE)
• adaptive thresholding
• closed-form estimator
• sample-limited regime