Tractable Structure Search in the Presence of Latent Variables

Thomas Richardson, Heiko Bailer, Moulinath Banarjees
Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics, PMLR R2, 1999.

Abstract

The problem of learning the structure of a DAG model in the presence of latent variables presents many formidable challenges. In particular there are an infinite number of latent variable models to consider, and these models possess features which make them hard to work with. We describe a class of graphical models which can represent the conditional independence structure induced by a latent variable model over the observed margin. We give a parametrization of the set of Gaussian distributions with conditional independence structure given by a MAG model. The models are illustrated via a simple example. Different estimation techniques are discussed in the context of Zellner’s Seemingly Unrelated Regression (SUR) models.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR2-richardson99a, title = {Tractable Structure Search in the Presence of Latent Variables}, author = {Richardson, Thomas and Bailer, Heiko and Banarjees, Moulinath}, 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/richardson99a/richardson99a.pdf}, url = {https://proceedings.mlr.press/r2/richardson99a.html}, abstract = {The problem of learning the structure of a DAG model in the presence of latent variables presents many formidable challenges. In particular there are an infinite number of latent variable models to consider, and these models possess features which make them hard to work with. We describe a class of graphical models which can represent the conditional independence structure induced by a latent variable model over the observed margin. We give a parametrization of the set of Gaussian distributions with conditional independence structure given by a MAG model. The models are illustrated via a simple example. Different estimation techniques are discussed in the context of Zellner’s Seemingly Unrelated Regression (SUR) models.}, note = {Reissued by PMLR on 20 August 2020.} }
Endnote
%0 Conference Paper %T Tractable Structure Search in the Presence of Latent Variables %A Thomas Richardson %A Heiko Bailer %A Moulinath Banarjees %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-richardson99a %I PMLR %U https://proceedings.mlr.press/r2/richardson99a.html %V R2 %X The problem of learning the structure of a DAG model in the presence of latent variables presents many formidable challenges. In particular there are an infinite number of latent variable models to consider, and these models possess features which make them hard to work with. We describe a class of graphical models which can represent the conditional independence structure induced by a latent variable model over the observed margin. We give a parametrization of the set of Gaussian distributions with conditional independence structure given by a MAG model. The models are illustrated via a simple example. Different estimation techniques are discussed in the context of Zellner’s Seemingly Unrelated Regression (SUR) models. %Z Reissued by PMLR on 20 August 2020.
APA
Richardson, T., Bailer, H. & Banarjees, M.. (1999). Tractable Structure Search in the Presence of Latent 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/richardson99a.html. Reissued by PMLR on 20 August 2020.

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