On the Complexity of Strong and Epistemic Credal Networks

Denis Maua, Cassio de Campos, Alessio Benavoli, Alessandro Antonucci
Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, PMLR R11:155-164, 2013.

Abstract

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the ir- relevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that in- ferences under strong independence are NP- hard even in trees with ternary variables. We prove that under epistemic irrelevance the polynomial time complexity of inferences in credal trees is not likely to extend to more general models (e.g. singly connected networks). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding computational complexity.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR11-maua13a, title = {On the Complexity of Strong and Epistemic Credal Networks}, author = {Maua, Denis and de Campos, Cassio and Benavoli, Alessio and Antonucci, Alessandro}, booktitle = {Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence}, pages = {155--164}, year = {2013}, editor = {Nicholson, Ann and Smyth, Padhraic}, volume = {R11}, series = {Proceedings of Machine Learning Research}, month = {12--14 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r11/main/assets/maua13a/maua13a.pdf}, url = {https://proceedings.mlr.press/r11/maua13a.html}, abstract = {Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the ir- relevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that in- ferences under strong independence are NP- hard even in trees with ternary variables. We prove that under epistemic irrelevance the polynomial time complexity of inferences in credal trees is not likely to extend to more general models (e.g. singly connected networks). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding computational complexity.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T On the Complexity of Strong and Epistemic Credal Networks %A Denis Maua %A Cassio de Campos %A Alessio Benavoli %A Alessandro Antonucci %B Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2013 %E Ann Nicholson %E Padhraic Smyth %F pmlr-vR11-maua13a %I PMLR %P 155--164 %U https://proceedings.mlr.press/r11/maua13a.html %V R11 %X Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the ir- relevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that in- ferences under strong independence are NP- hard even in trees with ternary variables. We prove that under epistemic irrelevance the polynomial time complexity of inferences in credal trees is not likely to extend to more general models (e.g. singly connected networks). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding computational complexity. %Z Reissued by PMLR on 04 October 2026.
APA
Maua, D., de Campos, C., Benavoli, A. & Antonucci, A.. (2013). On the Complexity of Strong and Epistemic Credal Networks. Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R11:155-164 Available from https://proceedings.mlr.press/r11/maua13a.html. Reissued by PMLR on 04 October 2026.

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