Causality with Gates

An intervention on a variable removes the influences that usually have a causal effect on that variable. Gates [1] are a general-purpose graphical modelling notation for representing such context-specific independencies in the structure of a graphical model. We extend d-separation to cover gated graphical models and show that it subsumes do calculus [2] when gates are used to represent interventions. We also show how standard message passing inference algorithms, such as belief propagation, can be applied to the gated graph. This demonstrates that causal reasoning can be performed by probabilistic inference alone.