Causal Graph Discovery from Self and Mutually Exciting Time Series

TL;DR

This paper introduces a new method for discovering causal graphs from time series data using a generalized linear model and convex optimization, with guarantees and validation on real-world medical data.

Contribution

It presents a novel causal discovery approach combining a linear structural causal model with a stochastic VI formulation and confidence interval estimation, advancing interpretability and reliability.

Findings

Effective recovery of causal DAGs from time series data.

Competitive prediction performance with black-box models.

Validated on medical data for clinical surveillance.

Abstract

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.