Identification in Tree-shaped Linear Structural Causal Models
- URL: http://arxiv.org/abs/2203.01852v2
- Date: Fri, 4 Mar 2022 14:45:09 GMT
- Title: Identification in Tree-shaped Linear Structural Causal Models
- Authors: Benito van der Zander, Marcel Wien\"obst, Markus Bl\"aser, Maciej
Li\'skiewicz
- Abstract summary: We investigate models, whose directed component forms a tree, and show that missing cycles of bidirected edges can be used to identify the model.
We show how multiple missing cycles can be combined to obtain a unique solution.
- Score: 4.751074059099236
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Linear structural equation models represent direct causal effects as directed
edges and confounding factors as bidirected edges. An open problem is to
identify the causal parameters from correlations between the nodes. We
investigate models, whose directed component forms a tree, and show that there,
besides classical instrumental variables, missing cycles of bidirected edges
can be used to identify the model. They can yield systems of quadratic
equations that we explicitly solve to obtain one or two solutions for the
causal parameters of adjacent directed edges. We show how multiple missing
cycles can be combined to obtain a unique solution. This results in an
algorithm that can identify instances that previously required approaches based
on Gr\"obner bases, which have doubly-exponential time complexity in the number
of structural parameters.
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