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：我们提出一种广义线性结构因果模型，结合新型数据自适应线性正则化方法，从时间序列中恢复有向无环因果图。通过利用近期发展的随机单调变分不等式（VI）框架，我们将因果发现问题转化为一般凸优化问题。进一步地，我们通过求解线性程序建立置信区间，针对广泛非线性单调链接函数，发展了非渐近恢复保证与可量化不确定性。通过大量数值实验验证了理论结果，并展示了该方法具有竞争力的性能。更重要的是，我们证实了该方法在恢复脓毒症相关功能紊乱（SADs）高度可解释因果有向无环图方面的有效性，同时达到与XGBoost等强大"黑箱"模型相媲美的预测性能。因此，临床医生未来采用我们提出的方法对高风险患者进行持续监测的可能性将显著提升。