Bayesian Networks for Variable Groups

Pekka Parviainen, Samuel Kaski
Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR 52:380-391, 2016.

Abstract

Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form \empha priori known groups, chosen to represent different “views” to or aspects of the same entities, one may be more interested in modeling dependencies between groups of variables rather than between individual variables. Motivated by this, we study prospects of representing relationships between variable groups using Bayesian network structures. We show that for dependency structures between groups to be expressible exactly, the data have to satisfy the so-called groupwise faithfulness assumption. We also show that one cannot learn causal relations between groups using only groupwise conditional independencies, but also variable-wise relations are needed. Additionally, we present algorithms for finding the groupwise dependency structures.

Cite this Paper

BibTeX
@InProceedings{pmlr-v52-parviainen16, title = {{B}ayesian Networks for Variable Groups}, author = {Parviainen, Pekka and Kaski, Samuel}, booktitle = {Proceedings of the Eighth International Conference on Probabilistic Graphical Models}, pages = {380--391}, year = {2016}, editor = {Antonucci, Alessandro and Corani, Giorgio and Campos}, Cassio Polpo}, volume = {52}, series = {Proceedings of Machine Learning Research}, address = {Lugano, Switzerland}, month = {06--09 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v52/parviainen16.pdf}, url = {https://proceedings.mlr.press/v52/parviainen16.html}, abstract = {Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form \empha priori known groups, chosen to represent different “views” to or aspects of the same entities, one may be more interested in modeling dependencies between groups of variables rather than between individual variables. Motivated by this, we study prospects of representing relationships between variable groups using Bayesian network structures. We show that for dependency structures between groups to be expressible exactly, the data have to satisfy the so-called groupwise faithfulness assumption. We also show that one cannot learn causal relations between groups using only groupwise conditional independencies, but also variable-wise relations are needed. Additionally, we present algorithms for finding the groupwise dependency structures.} }
Endnote
%0 Conference Paper %T Bayesian Networks for Variable Groups %A Pekka Parviainen %A Samuel Kaski %B Proceedings of the Eighth International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2016 %E Alessandro Antonucci %E Giorgio Corani %E Cassio Polpo Campos} %F pmlr-v52-parviainen16 %I PMLR %P 380--391 %U https://proceedings.mlr.press/v52/parviainen16.html %V 52 %X Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form \empha priori known groups, chosen to represent different “views” to or aspects of the same entities, one may be more interested in modeling dependencies between groups of variables rather than between individual variables. Motivated by this, we study prospects of representing relationships between variable groups using Bayesian network structures. We show that for dependency structures between groups to be expressible exactly, the data have to satisfy the so-called groupwise faithfulness assumption. We also show that one cannot learn causal relations between groups using only groupwise conditional independencies, but also variable-wise relations are needed. Additionally, we present algorithms for finding the groupwise dependency structures.
RIS
TY - CPAPER TI - Bayesian Networks for Variable Groups AU - Pekka Parviainen AU - Samuel Kaski BT - Proceedings of the Eighth International Conference on Probabilistic Graphical Models DA - 2016/08/15 ED - Alessandro Antonucci ED - Giorgio Corani ED - Cassio Polpo Campos} ID - pmlr-v52-parviainen16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 52 SP - 380 EP - 391 L1 - http://proceedings.mlr.press/v52/parviainen16.pdf UR - https://proceedings.mlr.press/v52/parviainen16.html AB - Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form \empha priori known groups, chosen to represent different “views” to or aspects of the same entities, one may be more interested in modeling dependencies between groups of variables rather than between individual variables. Motivated by this, we study prospects of representing relationships between variable groups using Bayesian network structures. We show that for dependency structures between groups to be expressible exactly, the data have to satisfy the so-called groupwise faithfulness assumption. We also show that one cannot learn causal relations between groups using only groupwise conditional independencies, but also variable-wise relations are needed. Additionally, we present algorithms for finding the groupwise dependency structures. ER -
APA
Parviainen, P. & Kaski, S.. (2016). Bayesian Networks for Variable Groups. Proceedings of the Eighth International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 52:380-391 Available from https://proceedings.mlr.press/v52/parviainen16.html.

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