Identifiability and Consistency of Bayesian Network Structure Learning from Incomplete Data

Tjebbe Bodewes, Marco Scutari
Proceedings of the 10th International Conference on Probabilistic Graphical Models, PMLR 138:29-40, 2020.

Abstract

Bayesian network (BN) structure learning from complete data has been extensively studied in the literature. However, fewer theoretical results are available for incomplete data, and most are based on the use of the Expectation-Maximisation (EM) algorithm. Balov (2013) proposed an alternative approach called Node-Average Likelihood (NAL) that is competitive with EM but computationally more efficient; and proved its consistency and model identifiability for discrete BNs. In this paper, we give general sufficient conditions for the consistency of NAL; and we prove consistency and identifiability for conditional Gaussian BNs, which include discrete and Gaussian BNs as special cases. Hence NAL has a wider applicability than originally stated in Balov (2013).

Cite this Paper

BibTeX
@InProceedings{pmlr-v138-bodewes20a, title = {Identifiability and Consistency of Bayesian Network Structure Learning from Incomplete Data}, author = {Bodewes, Tjebbe and Scutari, Marco}, booktitle = {Proceedings of the 10th International Conference on Probabilistic Graphical Models}, pages = {29--40}, year = {2020}, editor = {Jaeger, Manfred and Nielsen, Thomas Dyhre}, volume = {138}, series = {Proceedings of Machine Learning Research}, month = {23--25 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v138/bodewes20a/bodewes20a.pdf}, url = {https://proceedings.mlr.press/v138/bodewes20a.html}, abstract = {Bayesian network (BN) structure learning from complete data has been extensively studied in the literature. However, fewer theoretical results are available for incomplete data, and most are based on the use of the Expectation-Maximisation (EM) algorithm. Balov (2013) proposed an alternative approach called Node-Average Likelihood (NAL) that is competitive with EM but computationally more efficient; and proved its consistency and model identifiability for discrete BNs. In this paper, we give general sufficient conditions for the consistency of NAL; and we prove consistency and identifiability for conditional Gaussian BNs, which include discrete and Gaussian BNs as special cases. Hence NAL has a wider applicability than originally stated in Balov (2013).} }
Endnote
%0 Conference Paper %T Identifiability and Consistency of Bayesian Network Structure Learning from Incomplete Data %A Tjebbe Bodewes %A Marco Scutari %B Proceedings of the 10th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2020 %E Manfred Jaeger %E Thomas Dyhre Nielsen %F pmlr-v138-bodewes20a %I PMLR %P 29--40 %U https://proceedings.mlr.press/v138/bodewes20a.html %V 138 %X Bayesian network (BN) structure learning from complete data has been extensively studied in the literature. However, fewer theoretical results are available for incomplete data, and most are based on the use of the Expectation-Maximisation (EM) algorithm. Balov (2013) proposed an alternative approach called Node-Average Likelihood (NAL) that is competitive with EM but computationally more efficient; and proved its consistency and model identifiability for discrete BNs. In this paper, we give general sufficient conditions for the consistency of NAL; and we prove consistency and identifiability for conditional Gaussian BNs, which include discrete and Gaussian BNs as special cases. Hence NAL has a wider applicability than originally stated in Balov (2013).
APA
Bodewes, T. & Scutari, M.. (2020). Identifiability and Consistency of Bayesian Network Structure Learning from Incomplete Data. Proceedings of the 10th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 138:29-40 Available from https://proceedings.mlr.press/v138/bodewes20a.html.

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