Algebraic Equivalence of Linear Structural Equation Models

Joris M. Mooij, Thijs van Ommen

Publication date: 10 July 2018

Abstract: Despite their popularity, many questions about the algebraic constraints imposed by linear structural equation models remain open problems. For causal discovery, two of these problems are especially important: the enumeration of the constraints imposed by a model, and deciding whether two graphs define the same statistical model. We show how the half-trek criterion can be used to make progress in both of these problems. We apply our theoretical results to a small-scale model selection problem, and find that taking the additional algebraic constraints into account may lead to significant improvements in model selection accuracy.

Has companion code repository: https://github.com/caus-am/aelsem

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