Causal Graph Discovery from Self and Mutually Exciting Time Series
This addresses the need for interpretable causal discovery in time series data, particularly for clinical applications like sepsis monitoring, though it appears incremental as it builds on existing formulations with new regularization.
The paper tackles the problem of recovering causal directed acyclic graphs from time series data, developing a method that achieves competitive prediction performance comparable to XGBoost while providing interpretable causal graphs for Sepsis Associated Derangements.
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.