Conditional Independence in Testing Bayesian Networks

Yujia Shen, Haiying Huang, Arthur Choi, Adnan Darwiche
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:5701-5709, 2019.

Abstract

Testing Bayesian Networks (TBNs) were introduced recently to represent a set of distributions, one of which is selected based on the given evidence and used for reasoning. TBNs are more expressive than classical Bayesian Networks (BNs): Marginal queries correspond to multi-linear functions in BNs and to piecewise multi-linear functions in TBNs. Moreover, TBN queries are universal approximators, like neural networks. In this paper, we study conditional independence in TBNs, showing that it can be inferred from d-separation as in BNs. We also study the role of TBN expressiveness and independence in dealing with the problem of learning with incomplete models (i.e., ones that miss nodes or edges from the data-generating model). Finally, we illustrate our results on a number of concrete examples, including a case study on Hidden Markov Models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-shen19a, title = {Conditional Independence in Testing {B}ayesian Networks}, author = {Shen, Yujia and Huang, Haiying and Choi, Arthur and Darwiche, Adnan}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {5701--5709}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/shen19a/shen19a.pdf}, url = {https://proceedings.mlr.press/v97/shen19a.html}, abstract = {Testing Bayesian Networks (TBNs) were introduced recently to represent a set of distributions, one of which is selected based on the given evidence and used for reasoning. TBNs are more expressive than classical Bayesian Networks (BNs): Marginal queries correspond to multi-linear functions in BNs and to piecewise multi-linear functions in TBNs. Moreover, TBN queries are universal approximators, like neural networks. In this paper, we study conditional independence in TBNs, showing that it can be inferred from d-separation as in BNs. We also study the role of TBN expressiveness and independence in dealing with the problem of learning with incomplete models (i.e., ones that miss nodes or edges from the data-generating model). Finally, we illustrate our results on a number of concrete examples, including a case study on Hidden Markov Models.} }
Endnote
%0 Conference Paper %T Conditional Independence in Testing Bayesian Networks %A Yujia Shen %A Haiying Huang %A Arthur Choi %A Adnan Darwiche %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-shen19a %I PMLR %P 5701--5709 %U https://proceedings.mlr.press/v97/shen19a.html %V 97 %X Testing Bayesian Networks (TBNs) were introduced recently to represent a set of distributions, one of which is selected based on the given evidence and used for reasoning. TBNs are more expressive than classical Bayesian Networks (BNs): Marginal queries correspond to multi-linear functions in BNs and to piecewise multi-linear functions in TBNs. Moreover, TBN queries are universal approximators, like neural networks. In this paper, we study conditional independence in TBNs, showing that it can be inferred from d-separation as in BNs. We also study the role of TBN expressiveness and independence in dealing with the problem of learning with incomplete models (i.e., ones that miss nodes or edges from the data-generating model). Finally, we illustrate our results on a number of concrete examples, including a case study on Hidden Markov Models.
APA
Shen, Y., Huang, H., Choi, A. & Darwiche, A.. (2019). Conditional Independence in Testing Bayesian Networks. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:5701-5709 Available from https://proceedings.mlr.press/v97/shen19a.html.

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