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，并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（DAGs）。通过利用最近开发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个通用的凸优化问题。进一步地，我们通过求解线性规划建立了非渐近恢复保证与可量化不确定性，从而为广泛的一类非线性单调连接函数构建置信区间。我们通过大量数值实验验证了理论结果，并展示了所提方法的竞争性性能。最重要的是，我们证明了该方法在恢复与脓毒症相关功能紊乱（SADs）的高度可解释因果DAG方面具有显著效果，同时实现了与XGBoost等强大“黑箱”模型相当的预测性能。因此，未来临床医生更有可能采用我们的方法对高危患者进行持续性监护。