Learning Noisy-Or Networks with an Application in Linguistics

František Kratochvíl, Václav Kratochvíl, Jiří Vomlel
Proceedings of The 11th International Conference on Probabilistic Graphical Models, PMLR 186:277-288, 2022.

Abstract

In this paper we discuss the issue of learning Bayesian networks whose conditional probability tables (CPTs) are either noisy-or models or general CPTs. We refer to these models as Mixed Noisy-Or Bayesian Networks. In order to learn the structure of such Bayesian networks we modify the Bayesian Information Criteria (BIC) used for general Bayesian networks so that it reflects the number of parameters of a noisy-or model. We prove the log-likelihood function of a noisy-or model has a unique maximum and adapt the EM-learning method for leaky noisy-or models. We evaluate the proposed approach on synthetic data where it performs substantially better than general BNs. We apply this approach also to a problem from the domain of linguistics. We use Mixed Noisy-Or Bayesian Networks to model spread of loanwords in the South-East Asia Archipelago. We perform numerical experiments in which we compare prediction ability of general Bayesian Networks with Mixed Noisy-Or Bayesian Networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v186-kratochvil22a, title = {Learning Noisy-Or Networks with an Application in Linguistics}, author = {Kratochv\'{i}l, Franti\v{s}ek and Kratochv\'{i}l, V\'{a}clav and Vomlel, Ji\v{r}\'i}, booktitle = {Proceedings of The 11th International Conference on Probabilistic Graphical Models}, pages = {277--288}, year = {2022}, editor = {Salmerón, Antonio and Rumı́, Rafael}, volume = {186}, series = {Proceedings of Machine Learning Research}, month = {05--07 Oct}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v186/kratochvil22a/kratochvil22a.pdf}, url = {https://proceedings.mlr.press/v186/kratochvil22a.html}, abstract = {In this paper we discuss the issue of learning Bayesian networks whose conditional probability tables (CPTs) are either noisy-or models or general CPTs. We refer to these models as Mixed Noisy-Or Bayesian Networks. In order to learn the structure of such Bayesian networks we modify the Bayesian Information Criteria (BIC) used for general Bayesian networks so that it reflects the number of parameters of a noisy-or model. We prove the log-likelihood function of a noisy-or model has a unique maximum and adapt the EM-learning method for leaky noisy-or models. We evaluate the proposed approach on synthetic data where it performs substantially better than general BNs. We apply this approach also to a problem from the domain of linguistics. We use Mixed Noisy-Or Bayesian Networks to model spread of loanwords in the South-East Asia Archipelago. We perform numerical experiments in which we compare prediction ability of general Bayesian Networks with Mixed Noisy-Or Bayesian Networks.} }
Endnote
%0 Conference Paper %T Learning Noisy-Or Networks with an Application in Linguistics %A František Kratochvíl %A Václav Kratochvíl %A Jiří Vomlel %B Proceedings of The 11th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2022 %E Antonio Salmerón %E Rafael Rumı́ %F pmlr-v186-kratochvil22a %I PMLR %P 277--288 %U https://proceedings.mlr.press/v186/kratochvil22a.html %V 186 %X In this paper we discuss the issue of learning Bayesian networks whose conditional probability tables (CPTs) are either noisy-or models or general CPTs. We refer to these models as Mixed Noisy-Or Bayesian Networks. In order to learn the structure of such Bayesian networks we modify the Bayesian Information Criteria (BIC) used for general Bayesian networks so that it reflects the number of parameters of a noisy-or model. We prove the log-likelihood function of a noisy-or model has a unique maximum and adapt the EM-learning method for leaky noisy-or models. We evaluate the proposed approach on synthetic data where it performs substantially better than general BNs. We apply this approach also to a problem from the domain of linguistics. We use Mixed Noisy-Or Bayesian Networks to model spread of loanwords in the South-East Asia Archipelago. We perform numerical experiments in which we compare prediction ability of general Bayesian Networks with Mixed Noisy-Or Bayesian Networks.
APA
Kratochvíl, F., Kratochvíl, V. & Vomlel, J.. (2022). Learning Noisy-Or Networks with an Application in Linguistics. Proceedings of The 11th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 186:277-288 Available from https://proceedings.mlr.press/v186/kratochvil22a.html.

Related Material