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Additional LV-DAG simplification algorithms
In addition to the Robin Evans set of simplification algorithms for latent variable DAGs, we can do a couple things:
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If there are two latent variables U1 and U2 such that U1's only child is U2 and U2's only parent is U1, they can be merged into a new latent variable
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what you have to be worried about is if a latent variable U3 has two latents U1 and U2 as parents. This is a collider structure, so U1 and U2 should not be merged (slack discussion)
Turns out we don't need to do LV-LV contraction if you apply Evans rule 2 iteratively with a topological sort order
Example:
A -> B* -> C* -> D -> E
Apply 2
B*'
\
A -> C* -> D -> E
Apply 1
C*
\
A -> D -> E