Dynamic Structural Causal Models

TL;DR

This paper introduces Dynamic Structural Causal Models (DSCMs) for representing complex time-dependent systems, including cyclic and latent confounded systems, and explores their applications in causal inference and analysis of time-series data.

Contribution

It defines DSCMs for dynamic, possibly cyclic, systems with latent confounding, and develops tools like time-splitting and subsampling for causal analysis in continuous and discrete time.

Findings

Graphical Markov property for SDE systems

Methods for analyzing local independence and Granger causality

Guidelines for causal effect identification in time-series

Abstract

We study a specific type of SCM, called a Dynamic Structural Causal Model (DSCM), whose endogenous variables represent functions of time, which is possibly cyclic and allows for latent confounding. As a motivating use-case, we show that certain systems of Stochastic Differential Equations (SDEs) can be appropriately represented with DSCMs. An immediate consequence of this construction is a graphical Markov property for systems of SDEs. We define a time-splitting operation, allowing us to analyse the concept of local independence (a notion of continuous-time Granger (non-)causality). We also define a subsampling operation, which returns a discrete-time DSCM, and which can be used for mathematical analysis of subsampled time-series. We give suggestions how DSCMs can be used for identification of the causal effect of time-dependent interventions, and how existing constraint-based causal discovery algorithms can be applied to time-series data.