Learning networks determined by the ratio of prior and data

Maomi Ueno
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:605-612, 2010.

Abstract

Recent reports have described that the equiv- alent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymp- totic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size deter- mine the penalty of adding arcs in learning Bayesian networks. The number of arcs in- creases monotonically as the ESS increases; the number of arcs monotonically decreases as the ESS decreases. Furthermore, the marginal likelihood score provides a unified expression of various score metrics by chang- ing prior knowledge.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-ueno10a, title = {Learning networks determined by the ratio of prior and data}, author = {Ueno, Maomi}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {605--612}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/ueno10a/ueno10a.pdf}, url = {https://proceedings.mlr.press/r8/ueno10a.html}, abstract = {Recent reports have described that the equiv- alent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymp- totic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size deter- mine the penalty of adding arcs in learning Bayesian networks. The number of arcs in- creases monotonically as the ESS increases; the number of arcs monotonically decreases as the ESS decreases. Furthermore, the marginal likelihood score provides a unified expression of various score metrics by chang- ing prior knowledge.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Learning networks determined by the ratio of prior and data %A Maomi Ueno %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-ueno10a %I PMLR %P 605--612 %U https://proceedings.mlr.press/r8/ueno10a.html %V R8 %X Recent reports have described that the equiv- alent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymp- totic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size deter- mine the penalty of adding arcs in learning Bayesian networks. The number of arcs in- creases monotonically as the ESS increases; the number of arcs monotonically decreases as the ESS decreases. Furthermore, the marginal likelihood score provides a unified expression of various score metrics by chang- ing prior knowledge. %Z Reissued by PMLR on 04 October 2026.
APA
Ueno, M.. (2010). Learning networks determined by the ratio of prior and data. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:605-612 Available from https://proceedings.mlr.press/r8/ueno10a.html. Reissued by PMLR on 04 October 2026.

Related Material