Causal Graph Discovery from Self and Mutually Exciting Time Series
This work addresses the challenge of causal discovery in time series for domains like healthcare, enabling more interpretable models for clinicians, though it appears incremental as it builds on existing variational inequality formulations.
The paper tackles the problem of recovering causal directed acyclic graphs from time series data, using a generalized linear structural causal model with data-adaptive regularization, and demonstrates effectiveness in recovering interpretable causal graphs for Sepsis Associated Derangements while achieving prediction performance comparable to XGBoost.
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.