Learning Linear Bayesian Networks with Latent Variables

Animashree Anandkumar, Daniel Hsu, Adel Javanmard, Sham Kakade
; Proceedings of the 30th International Conference on Machine Learning, PMLR 28(1):249-257, 2013.

Abstract

This work considers the problem of learning linear Bayesian networks when some of the variables are unobserved. Identifiability and efficient recovery from low-order observable moments are established under a novel graphical constraint. The constraint concerns the expansion properties of the underlying directed acyclic graph (DAG) between observed and unobserved variables in the network, and it is satisfied by many natural families of DAGs that include multi-level DAGs, DAGs with effective depth one, as well as certain families of polytrees.

Cite this Paper


BibTeX
@InProceedings{pmlr-v28-anandkumar13, title = {Learning Linear Bayesian Networks with Latent Variables}, author = {Animashree Anandkumar and Daniel Hsu and Adel Javanmard and Sham Kakade}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {249--257}, year = {2013}, editor = {Sanjoy Dasgupta and David McAllester}, volume = {28}, number = {1}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/anandkumar13.pdf}, url = {http://proceedings.mlr.press/v28/anandkumar13.html}, abstract = {This work considers the problem of learning linear Bayesian networks when some of the variables are unobserved. Identifiability and efficient recovery from low-order observable moments are established under a novel graphical constraint. The constraint concerns the expansion properties of the underlying directed acyclic graph (DAG) between observed and unobserved variables in the network, and it is satisfied by many natural families of DAGs that include multi-level DAGs, DAGs with effective depth one, as well as certain families of polytrees. } }
Endnote
%0 Conference Paper %T Learning Linear Bayesian Networks with Latent Variables %A Animashree Anandkumar %A Daniel Hsu %A Adel Javanmard %A Sham Kakade %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-anandkumar13 %I PMLR %J Proceedings of Machine Learning Research %P 249--257 %U http://proceedings.mlr.press %V 28 %N 1 %W PMLR %X This work considers the problem of learning linear Bayesian networks when some of the variables are unobserved. Identifiability and efficient recovery from low-order observable moments are established under a novel graphical constraint. The constraint concerns the expansion properties of the underlying directed acyclic graph (DAG) between observed and unobserved variables in the network, and it is satisfied by many natural families of DAGs that include multi-level DAGs, DAGs with effective depth one, as well as certain families of polytrees.
RIS
TY - CPAPER TI - Learning Linear Bayesian Networks with Latent Variables AU - Animashree Anandkumar AU - Daniel Hsu AU - Adel Javanmard AU - Sham Kakade BT - Proceedings of the 30th International Conference on Machine Learning PY - 2013/02/13 DA - 2013/02/13 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-anandkumar13 PB - PMLR SP - 249 DP - PMLR EP - 257 L1 - http://proceedings.mlr.press/v28/anandkumar13.pdf UR - http://proceedings.mlr.press/v28/anandkumar13.html AB - This work considers the problem of learning linear Bayesian networks when some of the variables are unobserved. Identifiability and efficient recovery from low-order observable moments are established under a novel graphical constraint. The constraint concerns the expansion properties of the underlying directed acyclic graph (DAG) between observed and unobserved variables in the network, and it is satisfied by many natural families of DAGs that include multi-level DAGs, DAGs with effective depth one, as well as certain families of polytrees. ER -
APA
Anandkumar, A., Hsu, D., Javanmard, A. & Kakade, S.. (2013). Learning Linear Bayesian Networks with Latent Variables. Proceedings of the 30th International Conference on Machine Learning, in PMLR 28(1):249-257

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