  Obtaining a non-parametric expression for an interventional distribution is
one of the most fundamental tasks in causal inference. Such an expression can
be obtained for an identifiable causal effect by an algorithm or by manual
application of do-calculus. Often we are left with a complicated expression
which can lead to biased or inefficient estimates when missing data or
measurement errors are involved. We present an automatic simplification
algorithm that seeks to eliminate symbolically unnecessary variables from these
expressions by taking advantage of the structure of the underlying graphical
model. Our method is applicable to all causal effect formulas and is readily
available in the R package causaleffect.
