Integrating Markov process and structural causal models enables counterfactual inference in complex systems

Abstract

Modeling causal relationships between components of dynamic systems helps predict the outcomes of interventions on the system. Upon an intervention, many systems reach a new equilibrium state. Once the equilibrium is observed, counterfactual inference predicts ways in which the equilibrium would have differed under another intervention. Counterfactual inference is key for optimal selection of interventions that yield the desired equilibrium state. Complex dynamic systems are often described with Markov process (mechanistic) models, expressed as systems of ordinary or stochastic differential equations. They mimic interventions but do not support counterfactual inference. An alternative representation relies on structural causal models (SCMs). SCMs can represent the system at equilibrium, only require equi- librium data for parameter estimation, and support counterfactual inference. Unfortunately, multiple SCMs can represent the same observational or interventional distributions but provide different counterfactual insights. This drawback limits their practical use. Recent work has shown that for a Markov process with steady-state solution, it is possible to cast the system as an SCM. Using two complex biomolecular systems, this thesis illustrates the steps of the approach and its implementation in the probabilistic programming language Pyro, scalable to realistic Markov process models with nonlinear dynamics. The SCM is defined in terms of the parameters and of the equilibrium dynamics of the Markov process model, and counterfactual inference flows from these settings. We further discuss different inference techniques for counterfactual inference and evaluate the identifiability of SCM via different experimental approaches and sensitivity analysis.