Hidden Node Detection between Two Observable Nodes Based on Bayesian Clustering

Keisuke Yamazaki, Yoichi Motomura
; Proceedings of The 3rd International Workshop on Advanced Methodologies for Bayesian Networks, PMLR 73:165-175, 2017.

Abstract

The structure learning is one of the main concerns in studies of the Bayesian networks. In the present paper, we consider the network consisting of both observable and hidden nodes, and propose a method to investigate the existence of a hidden node between two observable nodes, which is the model selection problem between the networks with and without the middle hidden node. When the network includes a hidden node, it has been known that there are singularities in the parameter space, and the Fisher information matrix is not positive definite. Then, the many conventional criteria for the structure learning based on the Laplace approximation do not work. The proposed method is based on the Bayesian clustering, and its asymptotic property justifies the result; the redundant labels are eliminated and the simplest structure is detected even if there are singularities.

Cite this Paper


BibTeX
@InProceedings{pmlr-v73-yamazaki17a, title = {Hidden Node Detection between Two Observable Nodes Based on Bayesian Clustering}, author = {Keisuke Yamazaki and Yoichi Motomura}, booktitle = {Proceedings of The 3rd International Workshop on Advanced Methodologies for Bayesian Networks}, pages = {165--175}, year = {2017}, editor = {Antti Hyttinen and Joe Suzuki and Brandon Malone}, volume = {73}, series = {Proceedings of Machine Learning Research}, month = {20--22 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v73/yamazaki17a/yamazaki17a.pdf}, url = {http://proceedings.mlr.press/v73/yamazaki17a.html}, abstract = {The structure learning is one of the main concerns in studies of the Bayesian networks. In the present paper, we consider the network consisting of both observable and hidden nodes, and propose a method to investigate the existence of a hidden node between two observable nodes, which is the model selection problem between the networks with and without the middle hidden node. When the network includes a hidden node, it has been known that there are singularities in the parameter space, and the Fisher information matrix is not positive definite. Then, the many conventional criteria for the structure learning based on the Laplace approximation do not work. The proposed method is based on the Bayesian clustering, and its asymptotic property justifies the result; the redundant labels are eliminated and the simplest structure is detected even if there are singularities.} }
Endnote
%0 Conference Paper %T Hidden Node Detection between Two Observable Nodes Based on Bayesian Clustering %A Keisuke Yamazaki %A Yoichi Motomura %B Proceedings of The 3rd International Workshop on Advanced Methodologies for Bayesian Networks %C Proceedings of Machine Learning Research %D 2017 %E Antti Hyttinen %E Joe Suzuki %E Brandon Malone %F pmlr-v73-yamazaki17a %I PMLR %J Proceedings of Machine Learning Research %P 165--175 %U http://proceedings.mlr.press %V 73 %W PMLR %X The structure learning is one of the main concerns in studies of the Bayesian networks. In the present paper, we consider the network consisting of both observable and hidden nodes, and propose a method to investigate the existence of a hidden node between two observable nodes, which is the model selection problem between the networks with and without the middle hidden node. When the network includes a hidden node, it has been known that there are singularities in the parameter space, and the Fisher information matrix is not positive definite. Then, the many conventional criteria for the structure learning based on the Laplace approximation do not work. The proposed method is based on the Bayesian clustering, and its asymptotic property justifies the result; the redundant labels are eliminated and the simplest structure is detected even if there are singularities.
APA
Yamazaki, K. & Motomura, Y.. (2017). Hidden Node Detection between Two Observable Nodes Based on Bayesian Clustering. Proceedings of The 3rd International Workshop on Advanced Methodologies for Bayesian Networks, in PMLR 73:165-175

Related Material