New Causal Models Address Ambiguity in Equilibrium Systems.

Traditional causal reasoning frameworks, such as Causal Bayesian Networks (CBNs) and Structural Causal Models (SCMs), struggle to accurately represent real-world systems operating at equilibrium, especially those with feedback loops that create cyclic causal dependencies. A key limitation is the ambiguity of standard "perfect interventions" (do(X=x)), where different ways of enforcing the same variable value can lead to distinct effects. To address this, researchers propose Bipartite Graphical Causal Models (BGCMs). This new framework encodes the structure of a system of equations using a bipartite graph, featuring both variable and equation nodes. Within BGCMs, interventions are precisely defined, specifying the exact equation to be replaced, the variable targeted, and its new value, thereby eliminating the ambiguity found in conventional methods. The paper demonstrates through a detailed case study of a physical system that BGCMs naturally correspond to distinct real-world interventions. It also formulates a new Markov property using a graphical separation criterion called B-separation, which leverages the functional determinism of equations. This framework extends to settings with non-random inputs and provides a do-calculus for reasoning about domain invariances, effectively generalizing existing CBNs and SCMs while preserving graphical causal reasoning capabilities.