Missing simplification rule in ID* or make_counterfactual_graph
djinnome opened this issue · 1 comments
On page 1963 of Complete identification methods for the causal hierarchy
(Fig. 9 (d)) has two C-components, $\{Y_{x, z} ; X\}$ and $\{W_{x, z}\}$ , $P(y_{x,z}, w_{x,z}, x' ) = P(y_{x, z,w}, x'_w )P(w_{x,z} )$, which can be simplified by removing redundant subscripts to $P(y_{z, w} , x' )P(w_x )$.
What step of the ID* or make_cg algorithm licenses this simplification?
In particular my implementation of the make_cg algorithm correctly simplifies $x'_w$ to $x'$, but it does not simplify $y_{x,z,w}$ to $y_{z,w}$. On one hand, if $x$ is a parent of $w$ and $w$ is a parent of $y$, and $y$ intervenes on $w$ and $x$, then clearly, it is sufficient to intervene on $w$ only. But where in the make_cg algorithm should I check for this condition?
If I do not check for this condition, then line 8 of ID* is true, and the algorithm throws an Inconsistent exception.
The is resolved by intervening on the Markov blanket of a district, instead of intervening on all nodes not in the district.