Credal Sum-Product Networks

Denis D. Mauá, Fabio G. Cozman, Diarmaid Conaty, Cassio P. Campos
Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:205-216, 2017.

Abstract

Sum-product networks are a relatively new and increasingly popular class of (precise) probabilistic graphical models that allow for marginal inference with polynomial effort. As with other probabilistic models, sum-product networks are often learned from data and used to perform classification. Hence, their results are prone to be unreliable and overconfident. In this work, we develop credal sum-product networks, an imprecise extension of sum-product networks. We present algorithms and complexity results for common inference tasks. We apply our algorithms on realistic classification task using images of digits and show that credal sum-product networks obtained by a perturbation of the parameters of learned sum-product networks are able to distinguish between reliable and unreliable classifications with high accuracy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v62-mauá17a, title = {Credal Sum-Product Networks}, author = {Mauá, Denis D. and Cozman, Fabio G. and Conaty, Diarmaid and Campos, Cassio P.}, booktitle = {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {205--216}, year = {2017}, editor = {Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien}, volume = {62}, series = {Proceedings of Machine Learning Research}, month = {10--14 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v62/mauá17a/mauá17a.pdf}, url = {https://proceedings.mlr.press/v62/mau%C3%A117a.html}, abstract = {Sum-product networks are a relatively new and increasingly popular class of (precise) probabilistic graphical models that allow for marginal inference with polynomial effort. As with other probabilistic models, sum-product networks are often learned from data and used to perform classification. Hence, their results are prone to be unreliable and overconfident. In this work, we develop credal sum-product networks, an imprecise extension of sum-product networks. We present algorithms and complexity results for common inference tasks. We apply our algorithms on realistic classification task using images of digits and show that credal sum-product networks obtained by a perturbation of the parameters of learned sum-product networks are able to distinguish between reliable and unreliable classifications with high accuracy.} }
Endnote
%0 Conference Paper %T Credal Sum-Product Networks %A Denis D. Mauá %A Fabio G. Cozman %A Diarmaid Conaty %A Cassio P. Campos %B Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2017 %E Alessandro Antonucci %E Giorgio Corani %E Inés Couso %E Sébastien Destercke %F pmlr-v62-mauá17a %I PMLR %P 205--216 %U https://proceedings.mlr.press/v62/mau%C3%A117a.html %V 62 %X Sum-product networks are a relatively new and increasingly popular class of (precise) probabilistic graphical models that allow for marginal inference with polynomial effort. As with other probabilistic models, sum-product networks are often learned from data and used to perform classification. Hence, their results are prone to be unreliable and overconfident. In this work, we develop credal sum-product networks, an imprecise extension of sum-product networks. We present algorithms and complexity results for common inference tasks. We apply our algorithms on realistic classification task using images of digits and show that credal sum-product networks obtained by a perturbation of the parameters of learned sum-product networks are able to distinguish between reliable and unreliable classifications with high accuracy.
APA
Mauá, D.D., Cozman, F.G., Conaty, D. & Campos, C.P.. (2017). Credal Sum-Product Networks. Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 62:205-216 Available from https://proceedings.mlr.press/v62/mau%C3%A117a.html.

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