On the geometry of DAG models with hidden variables

Dan Geiger, David Heckerman, Henry King, Christopher Meek
Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics, PMLR R2, 1999.

Abstract

We prove that many graphical models with hidden variables are not curved exponential families. This result, together with the fact that some graphical models are curved and not linear, implies that the hierarchy of graphical models, as linear, curved, and stratified, is non-collapsing; each level in the hierarchy is strictly contained in the larger levels. This result is discussed in the context of model selection of graphical models.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR2-geiger99a, title = {On the geometry of {DAG} models with hidden variables}, author = {Geiger, Dan and Heckerman, David and King, Henry and Meek, Christopher}, booktitle = {Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics}, year = {1999}, editor = {Heckerman, David and Whittaker, Joe}, volume = {R2}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jan}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/r2/geiger99a/geiger99a.pdf}, url = {https://proceedings.mlr.press/r2/geiger99a.html}, abstract = {We prove that many graphical models with hidden variables are not curved exponential families. This result, together with the fact that some graphical models are curved and not linear, implies that the hierarchy of graphical models, as linear, curved, and stratified, is non-collapsing; each level in the hierarchy is strictly contained in the larger levels. This result is discussed in the context of model selection of graphical models.}, note = {Reissued by PMLR on 20 August 2020.} }
Endnote
%0 Conference Paper %T On the geometry of DAG models with hidden variables %A Dan Geiger %A David Heckerman %A Henry King %A Christopher Meek %B Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 1999 %E David Heckerman %E Joe Whittaker %F pmlr-vR2-geiger99a %I PMLR %U https://proceedings.mlr.press/r2/geiger99a.html %V R2 %X We prove that many graphical models with hidden variables are not curved exponential families. This result, together with the fact that some graphical models are curved and not linear, implies that the hierarchy of graphical models, as linear, curved, and stratified, is non-collapsing; each level in the hierarchy is strictly contained in the larger levels. This result is discussed in the context of model selection of graphical models. %Z Reissued by PMLR on 20 August 2020.
APA
Geiger, D., Heckerman, D., King, H. & Meek, C.. (1999). On the geometry of DAG models with hidden variables. Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R2 Available from https://proceedings.mlr.press/r2/geiger99a.html. Reissued by PMLR on 20 August 2020.

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