Faithfulness in Chain Graphs: The Gaussian Case

Jose M. Peña
Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, PMLR 15:588-599, 2011.

Abstract

This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that almost all the regular Gaussian distributions that factorize with respect to a chain graph are faithful to it. This result has three important consequences. First, chain graphs are more powerful than undirected graphs and acyclic directed graphs for representing regular Gaussian distributions, as some of these distributions can be represented exactly by the former but not by the latter. Second, the moralization and c-separation criteria for reading independencies from a chain graph are complete, in the sense that they identify all the independencies that can be identified from the chain graph alone. Third, some definitions of equivalence in chain graphs coincide and, thus, they have the same graphical characterization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v15-pena11a, title = {Faithfulness in Chain Graphs: The {G}aussian Case}, author = {Peña, Jose M.}, booktitle = {Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics}, pages = {588--599}, year = {2011}, editor = {Gordon, Geoffrey and Dunson, David and Dudík, Miroslav}, volume = {15}, series = {Proceedings of Machine Learning Research}, address = {Fort Lauderdale, FL, USA}, month = {11--13 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v15/pena11a/pena11a.pdf}, url = {https://proceedings.mlr.press/v15/pena11a.html}, abstract = {This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that almost all the regular Gaussian distributions that factorize with respect to a chain graph are faithful to it. This result has three important consequences. First, chain graphs are more powerful than undirected graphs and acyclic directed graphs for representing regular Gaussian distributions, as some of these distributions can be represented exactly by the former but not by the latter. Second, the moralization and c-separation criteria for reading independencies from a chain graph are complete, in the sense that they identify all the independencies that can be identified from the chain graph alone. Third, some definitions of equivalence in chain graphs coincide and, thus, they have the same graphical characterization.} }
Endnote
%0 Conference Paper %T Faithfulness in Chain Graphs: The Gaussian Case %A Jose M. Peña %B Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2011 %E Geoffrey Gordon %E David Dunson %E Miroslav Dudík %F pmlr-v15-pena11a %I PMLR %P 588--599 %U https://proceedings.mlr.press/v15/pena11a.html %V 15 %X This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that almost all the regular Gaussian distributions that factorize with respect to a chain graph are faithful to it. This result has three important consequences. First, chain graphs are more powerful than undirected graphs and acyclic directed graphs for representing regular Gaussian distributions, as some of these distributions can be represented exactly by the former but not by the latter. Second, the moralization and c-separation criteria for reading independencies from a chain graph are complete, in the sense that they identify all the independencies that can be identified from the chain graph alone. Third, some definitions of equivalence in chain graphs coincide and, thus, they have the same graphical characterization.
RIS
TY - CPAPER TI - Faithfulness in Chain Graphs: The Gaussian Case AU - Jose M. Peña BT - Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics DA - 2011/06/14 ED - Geoffrey Gordon ED - David Dunson ED - Miroslav Dudík ID - pmlr-v15-pena11a PB - PMLR DP - Proceedings of Machine Learning Research VL - 15 SP - 588 EP - 599 L1 - http://proceedings.mlr.press/v15/pena11a/pena11a.pdf UR - https://proceedings.mlr.press/v15/pena11a.html AB - This paper deals with chain graphs under the classic Lauritzen-Wermuth-Frydenberg interpretation. We prove that almost all the regular Gaussian distributions that factorize with respect to a chain graph are faithful to it. This result has three important consequences. First, chain graphs are more powerful than undirected graphs and acyclic directed graphs for representing regular Gaussian distributions, as some of these distributions can be represented exactly by the former but not by the latter. Second, the moralization and c-separation criteria for reading independencies from a chain graph are complete, in the sense that they identify all the independencies that can be identified from the chain graph alone. Third, some definitions of equivalence in chain graphs coincide and, thus, they have the same graphical characterization. ER -
APA
Peña, J.M.. (2011). Faithfulness in Chain Graphs: The Gaussian Case. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 15:588-599 Available from https://proceedings.mlr.press/v15/pena11a.html.

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