Counterfactual Resimulation for Causal Analysis of Rule-Based Models

Abstract

Models based on rules that express local and heterogeneous mechanisms of stochastic interactions between structured agents are an important tool for investigating the dynamical behavior of complex systems, especially in molecular biology. Given a simulated trace of events, the challenge is to construct a causal diagram that explains how a phenomenon of interest occurred. Counterfactual analysis can provide distinctive insights, but its standard definition is not applicable in rule-based models because they are not readily expressible in terms of structural equations. We provide a semantics of counterfactual statements that addresses this challenge by sampling counterfactual trajectories that are probabilistically as close to the factual trace as a given intervention permits them to be. We then show how counterfactual dependencies give rise to explanations in terms of relations of enablement and prevention between events.

“Minimal metabolism”: A key concept to investigate the origins and nature of biological systems

“…Furthermore, since the application of rules depends on specific structural patterns, as preconditions, this type of model is ideally suited to identify subsequent rule applications, necessary to obtain a particular event of interest as a result of a sequence of elementary steps (e.g., the synthesis of a complex molecule from simpler building blocks). This methodology is called "mechanistic causal analysis", [106,107] and permits extraction of meaningful pathways or mechanisms from ensembles of trajectories in rule-based simulations. The most recent theoretical advances in this line of work have been implemented as the Kappa Calculus, [108] a rule-based approach that operates on site graphs and has already been showcased (e.g., for the analysis of the synchronization of the molecular oscillators implementing the circadian clock of cyanobacteria [109] ).…”

Causality analysis and fault ascription in component-based systems

“…[9] specifies formal constraints on the behavior of preemption and overdetermination in SEM. In a similar spirit to our definition of counterfactuals, [26] defines the semantics of counterfactual analysis for traces of events of stochastic rule-based models. [23] proposes a general categorical formalization of interventions on a single variable.…”

Soft component automata: Composition, compilation, logic, and verification

“…Fontana et al [37] address the problem of finding causal relations among events in traces generated by stochastic simulation of rule based systems (specifically cell signaling systems modeled in the Kappa language). An event is the application of a rule instance in a particular context at particular time.…”