Graphical Representations for Algebraic Constraints of Linear Structural Equations Models

Thijs van Ommen, Mathias Drton
Proceedings of The 11th International Conference on Probabilistic Graphical Models, PMLR 186:409-420, 2022.

Abstract

The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical for many purposes. In this paper, we present a graphical notation for many of these polynomial constraints. The expressive power of this notation is investigated both theoretically and empirically.

Cite this Paper

BibTeX
@InProceedings{pmlr-v186-ommen22a, title = {Graphical Representations for Algebraic Constraints of Linear Structural Equations Models}, author = {van Ommen, Thijs and Drton, Mathias}, booktitle = {Proceedings of The 11th International Conference on Probabilistic Graphical Models}, pages = {409--420}, year = {2022}, editor = {Salmerón, Antonio and Rumı́, Rafael}, volume = {186}, series = {Proceedings of Machine Learning Research}, month = {05--07 Oct}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v186/ommen22a/ommen22a.pdf}, url = {https://proceedings.mlr.press/v186/ommen22a.html}, abstract = {The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical for many purposes. In this paper, we present a graphical notation for many of these polynomial constraints. The expressive power of this notation is investigated both theoretically and empirically.} }
Endnote
%0 Conference Paper %T Graphical Representations for Algebraic Constraints of Linear Structural Equations Models %A Thijs van Ommen %A Mathias Drton %B Proceedings of The 11th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2022 %E Antonio Salmerón %E Rafael Rumı́ %F pmlr-v186-ommen22a %I PMLR %P 409--420 %U https://proceedings.mlr.press/v186/ommen22a.html %V 186 %X The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical for many purposes. In this paper, we present a graphical notation for many of these polynomial constraints. The expressive power of this notation is investigated both theoretically and empirically.
APA
van Ommen, T. & Drton, M.. (2022). Graphical Representations for Algebraic Constraints of Linear Structural Equations Models. Proceedings of The 11th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 186:409-420 Available from https://proceedings.mlr.press/v186/ommen22a.html.

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