Closed-Form Learning of Markov Networks from Dependency Networks

Daniel Lowd
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:531-540, 2012.

Abstract

Markov networks (MNs) are a powerful way to compactly represent a joint probability distribution, but most MN structure learning methods are very slow, due to the high cost of evaluating candidates structures. Dependency networks (DNs) represent a probability distribution as a set of conditional probability distributions. DNs are very fast to learn, but the conditional distributions may be inconsistent with each other and few inference algorithms support DNs. In this paper, we present a closed-form method for converting a DN into an MN, allowing us to enjoy both the efficiency of DN learning and the convenience of the MN representation. When the DN is consistent, this conversion is exact. For inconsistent DNs, we present averaging methods that significantly improve the approximation. In experiments on 12 standard datasets, our methods are orders of magnitude faster than and often more accurate than combining conditional distributions using weight learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-lowd12a, title = {Closed-Form Learning of {M}arkov Networks from Dependency Networks}, author = {Lowd, Daniel}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {531--540}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/lowd12a/lowd12a.pdf}, url = {https://proceedings.mlr.press/r10/lowd12a.html}, abstract = {Markov networks (MNs) are a powerful way to compactly represent a joint probability distribution, but most MN structure learning methods are very slow, due to the high cost of evaluating candidates structures. Dependency networks (DNs) represent a probability distribution as a set of conditional probability distributions. DNs are very fast to learn, but the conditional distributions may be inconsistent with each other and few inference algorithms support DNs. In this paper, we present a closed-form method for converting a DN into an MN, allowing us to enjoy both the efficiency of DN learning and the convenience of the MN representation. When the DN is consistent, this conversion is exact. For inconsistent DNs, we present averaging methods that significantly improve the approximation. In experiments on 12 standard datasets, our methods are orders of magnitude faster than and often more accurate than combining conditional distributions using weight learning.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Closed-Form Learning of Markov Networks from Dependency Networks %A Daniel Lowd %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-lowd12a %I PMLR %P 531--540 %U https://proceedings.mlr.press/r10/lowd12a.html %V R10 %X Markov networks (MNs) are a powerful way to compactly represent a joint probability distribution, but most MN structure learning methods are very slow, due to the high cost of evaluating candidates structures. Dependency networks (DNs) represent a probability distribution as a set of conditional probability distributions. DNs are very fast to learn, but the conditional distributions may be inconsistent with each other and few inference algorithms support DNs. In this paper, we present a closed-form method for converting a DN into an MN, allowing us to enjoy both the efficiency of DN learning and the convenience of the MN representation. When the DN is consistent, this conversion is exact. For inconsistent DNs, we present averaging methods that significantly improve the approximation. In experiments on 12 standard datasets, our methods are orders of magnitude faster than and often more accurate than combining conditional distributions using weight learning. %Z Reissued by PMLR on 04 October 2026.
APA
Lowd, D.. (2012). Closed-Form Learning of Markov Networks from Dependency Networks. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:531-540 Available from https://proceedings.mlr.press/r10/lowd12a.html. Reissued by PMLR on 04 October 2026.

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