A Generalization of the Tetrad Representation Theorem

Glenn Shafer, Alexander Kogan, Peter Spirtes
Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, PMLR R0:476-487, 1995.

Abstract

The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and sufficient for the vanishing of an individual tetrad difference in a linear structural equation model. In this paper, we generalize their result from individual tetrad differences to sets of tetrad differences of a certain form, and we simplify their proof. The generalization allows tighter constraints to be placed on the set of linear models compatible with given data and thereby facilitates the search for parsimonious models for large data sets.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR0-shafer95a, title = {A Generalization of the Tetrad Representation Theorem}, author = {Shafer, Glenn and Kogan, Alexander and Spirtes, Peter}, booktitle = {Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics}, pages = {476--487}, year = {1995}, editor = {Fisher, Doug and Lenz, Hans-Joachim}, volume = {R0}, series = {Proceedings of Machine Learning Research}, month = {04--07 Jan}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/r0/shafer95a/shafer95a.pdf}, url = {https://proceedings.mlr.press/r0/shafer95a.html}, abstract = {The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and sufficient for the vanishing of an individual tetrad difference in a linear structural equation model. In this paper, we generalize their result from individual tetrad differences to sets of tetrad differences of a certain form, and we simplify their proof. The generalization allows tighter constraints to be placed on the set of linear models compatible with given data and thereby facilitates the search for parsimonious models for large data sets.}, note = {Reissued by PMLR on 01 May 2022.} }
Endnote
%0 Conference Paper %T A Generalization of the Tetrad Representation Theorem %A Glenn Shafer %A Alexander Kogan %A Peter Spirtes %B Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 1995 %E Doug Fisher %E Hans-Joachim Lenz %F pmlr-vR0-shafer95a %I PMLR %P 476--487 %U https://proceedings.mlr.press/r0/shafer95a.html %V R0 %X The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and sufficient for the vanishing of an individual tetrad difference in a linear structural equation model. In this paper, we generalize their result from individual tetrad differences to sets of tetrad differences of a certain form, and we simplify their proof. The generalization allows tighter constraints to be placed on the set of linear models compatible with given data and thereby facilitates the search for parsimonious models for large data sets. %Z Reissued by PMLR on 01 May 2022.
APA
Shafer, G., Kogan, A. & Spirtes, P.. (1995). A Generalization of the Tetrad Representation Theorem. Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R0:476-487 Available from https://proceedings.mlr.press/r0/shafer95a.html. Reissued by PMLR on 01 May 2022.

Related Material