Algebraic Equivalence of Linear Structural Equation Models

Thijs van Ommen, Joris M. Mooij
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:71-80, 2017.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-ommen17a, title = {Algebraic Equivalence of Linear Structural Equation Models}, author = {van Ommen, Thijs and Mooij, Joris M.}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {71--80}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/ommen17a/ommen17a.pdf}, url = {https://proceedings.mlr.press/r15/ommen17a.html}, 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Algebraic Equivalence of Linear Structural Equation Models %A Thijs van Ommen %A Joris M. Mooij %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-ommen17a %I PMLR %P 71--80 %U https://proceedings.mlr.press/r15/ommen17a.html %V R15 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
van Ommen, T. & Mooij, J.M.. (2017). Algebraic Equivalence of Linear Structural Equation Models. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:71-80 Available from https://proceedings.mlr.press/r15/ommen17a.html. Reissued by PMLR on 04 October 2026.

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