We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone Variational Inequality (VI) formulation, we cast the causal discovery problem as a general convex optimization. Furthermore, we develop a non-asymptotic recovery guarantee and quantifiable uncertainty by solving a linear program to establish confidence intervals for a wide range of non-linear monotone link functions. We validate our theoretical results and show the competitive performance of our method via extensive numerical experiments. Most importantly, we demonstrate the effectiveness of our approach in recovering highly interpretable causal DAGs over Sepsis Associated Derangements (SADs) while achieving comparable prediction performance to powerful ``black-box'' models such as XGBoost. Thus, the future adoption of our proposed method to conduct continuous surveillance of high-risk patients by clinicians is much more likely.

翻译：我们提出了一种广义线性结构因果模型，结合一种新颖的数据自适应线性正则化方法，用于从时间序列中恢复有向无环因果图（DAG）。通过利用最近发展的随机单调变分不等式（VI）公式，我们将因果发现问题转化为一般的凸优化问题。此外，我们通过求解线性规划为非线性的单调连接函数建立置信区间，从而开发了非渐近恢复保证和可量化的不确定性。通过广泛的数值实验，我们验证了理论结果并展示了方法的竞争性能。最重要的是，我们证明了该方法在恢复脓毒症相关器官功能障碍（SADs）高度可解释的因果DAG图方面的有效性，同时实现了与XGBoost等强大的"黑盒"模型相当的可预测性能。因此，临床医生未来更有可能采用我们提出的方法对高危患者进行持续监测。