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Additional LV-DAG simplification algorithms

Open cthoyt opened this issue 4 years ago • 1 comments

In addition to the Robin Evans set of simplification algorithms for latent variable DAGs, we can do a couple things:

  1. 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

  2. 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)

cthoyt avatar Mar 10 '21 15:03 cthoyt

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

cthoyt avatar Mar 10 '21 22:03 cthoyt