A Sequence of Relaxations Constraining Hidden Variable Models

Greg Ver Steeg, Aram Galstyan
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:790-799, 2011.

Abstract

Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that model. Our main contribution is to introduce a sequence of relaxations which provides progressively tighter hidden variable tests. We demonstrate applicability to mixtures of sequences of i.i.d. variables, Bell inequalities, and homophily models in social networks. For the last, we demonstrate that our method provides a test that is able to rule out latent homophily as the sole explanation for correlations on a real social network that are known to be due to influence.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-steeg11a, title = {A Sequence of Relaxations Constraining Hidden Variable Models}, author = {Steeg, Greg Ver and Galstyan, Aram}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {790--799}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/steeg11a/steeg11a.pdf}, url = {https://proceedings.mlr.press/r9/steeg11a.html}, abstract = {Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that model. Our main contribution is to introduce a sequence of relaxations which provides progressively tighter hidden variable tests. We demonstrate applicability to mixtures of sequences of i.i.d. variables, Bell inequalities, and homophily models in social networks. For the last, we demonstrate that our method provides a test that is able to rule out latent homophily as the sole explanation for correlations on a real social network that are known to be due to influence.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T A Sequence of Relaxations Constraining Hidden Variable Models %A Greg Ver Steeg %A Aram Galstyan %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-steeg11a %I PMLR %P 790--799 %U https://proceedings.mlr.press/r9/steeg11a.html %V R9 %X Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that model. Our main contribution is to introduce a sequence of relaxations which provides progressively tighter hidden variable tests. We demonstrate applicability to mixtures of sequences of i.i.d. variables, Bell inequalities, and homophily models in social networks. For the last, we demonstrate that our method provides a test that is able to rule out latent homophily as the sole explanation for correlations on a real social network that are known to be due to influence. %Z Reissued by PMLR on 04 October 2026.
APA
Steeg, G.V. & Galstyan, A.. (2011). A Sequence of Relaxations Constraining Hidden Variable Models. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:790-799 Available from https://proceedings.mlr.press/r9/steeg11a.html. Reissued by PMLR on 04 October 2026.

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