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 convex optimization approach, providing guarantees and uncertainty quantification, and demonstrating effectiveness on medical data.

Contribution

It presents a generalized linear causal discovery framework with a novel regularization and confidence interval estimation, advancing causal inference from time series.

Findings

Effective recovery of causal DAGs in simulations

Competitive prediction performance with black-box models

Successful application to clinical sepsis data

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.