An Empirical-Bayes Score for Discrete Bayesian Networks

Marco Scutari
Proceedings of the Eighth International Conference on Probabilistic Graphical Models, PMLR 52:438-448, 2016.

Abstract

Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the \emphmaximum a posteriori network as the learned model. For discrete Bayesian networks, the canonical choice for a posterior score is the Bayesian Dirichlet equivalent uniform (BDeu) marginal likelihood with a uniform (U) graph prior (Heckerman et al., 1995). Its favourable theoretical properties descend from assuming a uniform prior both on the space of the network structures and on the space of the parameters of the network. In this paper, we revisit the limitations of these assumptions and we introduce an alternative set of assumptions and the resulting score: the Bayesian Dirichlet sparse (BDs) empirical Bayes marginal likelihood with a marginal uniform (MU) graph prior. We evaluate its performance in an extensive simulation study, showing that MU+BDs is more accurate than U+BDeu both in learning the structure of the network and in predicting new observations, while not being computationally more complex to estimate.

Cite this Paper

BibTeX
@InProceedings{pmlr-v52-scutari16, title = {An Empirical-{B}ayes Score for Discrete {B}ayesian Networks}, author = {Scutari, Marco}, booktitle = {Proceedings of the Eighth International Conference on Probabilistic Graphical Models}, pages = {438--448}, 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/scutari16.pdf}, url = {https://proceedings.mlr.press/v52/scutari16.html}, abstract = {Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the \emphmaximum a posteriori network as the learned model. For discrete Bayesian networks, the canonical choice for a posterior score is the Bayesian Dirichlet equivalent uniform (BDeu) marginal likelihood with a uniform (U) graph prior (Heckerman et al., 1995). Its favourable theoretical properties descend from assuming a uniform prior both on the space of the network structures and on the space of the parameters of the network. In this paper, we revisit the limitations of these assumptions and we introduce an alternative set of assumptions and the resulting score: the Bayesian Dirichlet sparse (BDs) empirical Bayes marginal likelihood with a marginal uniform (MU) graph prior. We evaluate its performance in an extensive simulation study, showing that MU+BDs is more accurate than U+BDeu both in learning the structure of the network and in predicting new observations, while not being computationally more complex to estimate.} }
Endnote
%0 Conference Paper %T An Empirical-Bayes Score for Discrete Bayesian Networks %A Marco Scutari %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-scutari16 %I PMLR %P 438--448 %U https://proceedings.mlr.press/v52/scutari16.html %V 52 %X Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the \emphmaximum a posteriori network as the learned model. For discrete Bayesian networks, the canonical choice for a posterior score is the Bayesian Dirichlet equivalent uniform (BDeu) marginal likelihood with a uniform (U) graph prior (Heckerman et al., 1995). Its favourable theoretical properties descend from assuming a uniform prior both on the space of the network structures and on the space of the parameters of the network. In this paper, we revisit the limitations of these assumptions and we introduce an alternative set of assumptions and the resulting score: the Bayesian Dirichlet sparse (BDs) empirical Bayes marginal likelihood with a marginal uniform (MU) graph prior. We evaluate its performance in an extensive simulation study, showing that MU+BDs is more accurate than U+BDeu both in learning the structure of the network and in predicting new observations, while not being computationally more complex to estimate.
RIS
TY - CPAPER TI - An Empirical-Bayes Score for Discrete Bayesian Networks AU - Marco Scutari 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-scutari16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 52 SP - 438 EP - 448 L1 - http://proceedings.mlr.press/v52/scutari16.pdf UR - https://proceedings.mlr.press/v52/scutari16.html AB - Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the \emphmaximum a posteriori network as the learned model. For discrete Bayesian networks, the canonical choice for a posterior score is the Bayesian Dirichlet equivalent uniform (BDeu) marginal likelihood with a uniform (U) graph prior (Heckerman et al., 1995). Its favourable theoretical properties descend from assuming a uniform prior both on the space of the network structures and on the space of the parameters of the network. In this paper, we revisit the limitations of these assumptions and we introduce an alternative set of assumptions and the resulting score: the Bayesian Dirichlet sparse (BDs) empirical Bayes marginal likelihood with a marginal uniform (MU) graph prior. We evaluate its performance in an extensive simulation study, showing that MU+BDs is more accurate than U+BDeu both in learning the structure of the network and in predicting new observations, while not being computationally more complex to estimate. ER -
APA
Scutari, M.. (2016). An Empirical-Bayes Score for Discrete Bayesian Networks. Proceedings of the Eighth International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 52:438-448 Available from https://proceedings.mlr.press/v52/scutari16.html.

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