Identifying cause and effect in complex dynamic systems with hidden parts
Identifiability from Stationary Covariance in Linear SDEs with Reciprocal Interactions and Latent Variables
Machine Learning
Summary
Figuring out cause and effect in systems that change over time is very tricky, especially when some parts can't be observed and when things influence each other back and forth. This paper presents new rules that let us understand direct cause-effect links in such systems from data gathered when things settle down and stop changing. The authors also develop ways to spot cause relationships even when some variables are hidden, using tools called instrumental variables. Their work broadens what can be learned from stationary data in complex real-world systems.
What this means in practice
- •For control system engineers: Analyze systems with mutual interactions and hidden components to identify direct cause-effect relationships from steady-state observations.
- •For econometricians: Identify direct causal effects in economic models with feedback loops and latent factors using observational equilibrium data.
A theory result. No direct application yet.
Authors
Ana Leticia Garcez Vicente, Saber Salehkaleybar
Abstract
Continuous-time stochastic differential equations (SDEs) provide a natural framework for modeling interacting dynamical systems. A central causal question is whether causal effects among observed variables can be identified from observational data drawn from the stationary distribution, given the underlying causal graph. For linear SDEs, existing identifiability results are largely restricted to fully observed systems whose causal graphs contain no directed 2-cycles. We first establish new graphical conditions for the generic identifiability of causal effects in systems that may contain directed 2-cycles, thereby allowing for reciprocal interactions. Next, we address the previously unexplored setting of latent variables by developing an instrumental-variable framework for identifying a target direct causal effect under partial observability.