Causal Models with Constraints
This work addresses a specific problem for researchers in causal inference by enabling the modeling of constrained variables, though it is incremental as it builds on existing causal models.
The paper tackles the limitation of standard causal models in handling non-causal relationships, such as constraints like LDL+HDL=TOT, by extending them to allow constraints and defining a new intervention operation that disconnects variables from causal equations, resulting in a sound and complete axiomatization.
Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables $LDL$, $HDL$, and $TOT$ that represent the level of low-density lipoprotein cholesterol, the level of lipoprotein high-density lipoprotein cholesterol, and total cholesterol level, with the relation $LDL+HDL=TOT$. This cannot be done in standard causal models, because we can intervene simultaneously on all three variables. The goal of this paper is to extend standard causal models to allow for constraints on settings of variables. Although the extension is relatively straightforward, to make it useful we have to define a new intervention operation that $disconnects$ a variable from a causal equation. We give examples showing the usefulness of this extension, and provide a sound and complete axiomatization for causal models with constraints.