Bayesian Markov Blanket Estimation

Dinu Kaufmann, Sonali Parbhoo, Aleksander Wieczorek, Sebastian Keller, David Adametz, Volker Roth
; Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:333-341, 2016.

Abstract

This paper considers a Bayesian view for estimating the Markov blanket of a set of query variables, where the set of potential neighbours here is big. We factorize the posterior such that the Markov blanket is conditionally independent of the network of the potential neighbours. By exploiting this blockwise decoupling, we derive analytic expressions for posterior conditionals. Subsequently, we develop an inference scheme, which makes use of the factorization. As a result, estimation of a sub-network is possible without inferring an entire network. Since the resulting Gibbs sampler scales linearly with the number of variables, it can handle relatively large neighbourhoods. The proposed scheme results in faster convergence and superior mixing of the Markov chain than existing Bayesian network estimation techniques.

Cite this Paper


BibTeX
@InProceedings{pmlr-v51-kaufmann16, title = {Bayesian Markov Blanket Estimation}, author = {Dinu Kaufmann and Sonali Parbhoo and Aleksander Wieczorek and Sebastian Keller and David Adametz and Volker Roth}, booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics}, pages = {333--341}, year = {2016}, editor = {Arthur Gretton and Christian C. Robert}, volume = {51}, series = {Proceedings of Machine Learning Research}, address = {Cadiz, Spain}, month = {09--11 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v51/kaufmann16.pdf}, url = {http://proceedings.mlr.press/v51/kaufmann16.html}, abstract = {This paper considers a Bayesian view for estimating the Markov blanket of a set of query variables, where the set of potential neighbours here is big. We factorize the posterior such that the Markov blanket is conditionally independent of the network of the potential neighbours. By exploiting this blockwise decoupling, we derive analytic expressions for posterior conditionals. Subsequently, we develop an inference scheme, which makes use of the factorization. As a result, estimation of a sub-network is possible without inferring an entire network. Since the resulting Gibbs sampler scales linearly with the number of variables, it can handle relatively large neighbourhoods. The proposed scheme results in faster convergence and superior mixing of the Markov chain than existing Bayesian network estimation techniques.} }
Endnote
%0 Conference Paper %T Bayesian Markov Blanket Estimation %A Dinu Kaufmann %A Sonali Parbhoo %A Aleksander Wieczorek %A Sebastian Keller %A David Adametz %A Volker Roth %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-kaufmann16 %I PMLR %J Proceedings of Machine Learning Research %P 333--341 %U http://proceedings.mlr.press %V 51 %W PMLR %X This paper considers a Bayesian view for estimating the Markov blanket of a set of query variables, where the set of potential neighbours here is big. We factorize the posterior such that the Markov blanket is conditionally independent of the network of the potential neighbours. By exploiting this blockwise decoupling, we derive analytic expressions for posterior conditionals. Subsequently, we develop an inference scheme, which makes use of the factorization. As a result, estimation of a sub-network is possible without inferring an entire network. Since the resulting Gibbs sampler scales linearly with the number of variables, it can handle relatively large neighbourhoods. The proposed scheme results in faster convergence and superior mixing of the Markov chain than existing Bayesian network estimation techniques.
RIS
TY - CPAPER TI - Bayesian Markov Blanket Estimation AU - Dinu Kaufmann AU - Sonali Parbhoo AU - Aleksander Wieczorek AU - Sebastian Keller AU - David Adametz AU - Volker Roth BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics PY - 2016/05/02 DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-kaufmann16 PB - PMLR SP - 333 DP - PMLR EP - 341 L1 - http://proceedings.mlr.press/v51/kaufmann16.pdf UR - http://proceedings.mlr.press/v51/kaufmann16.html AB - This paper considers a Bayesian view for estimating the Markov blanket of a set of query variables, where the set of potential neighbours here is big. We factorize the posterior such that the Markov blanket is conditionally independent of the network of the potential neighbours. By exploiting this blockwise decoupling, we derive analytic expressions for posterior conditionals. Subsequently, we develop an inference scheme, which makes use of the factorization. As a result, estimation of a sub-network is possible without inferring an entire network. Since the resulting Gibbs sampler scales linearly with the number of variables, it can handle relatively large neighbourhoods. The proposed scheme results in faster convergence and superior mixing of the Markov chain than existing Bayesian network estimation techniques. ER -
APA
Kaufmann, D., Parbhoo, S., Wieczorek, A., Keller, S., Adametz, D. & Roth, V.. (2016). Bayesian Markov Blanket Estimation. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in PMLR 51:333-341

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