Robust Analysis of MAP Inference in Selective Sum-Product Networks

Julissa Giuliana Villanueva Llerena, Denis Deratani Mauá
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:430-440, 2019.

Abstract

Sum-Product Networks (SPN) are deep probabilistic models that have shown to achieve state-of-the-art performance in several machine learning tasks. As with many other probabilistic models, performing Maximum-A-Posteriori (MAP) inference is NP-hard in SPNs. A notable exception is selective SPNs, that constrain the network so as to allow MAP inference to be performed in linear time. Due to the high number of parameters, SPNs learned from data can produce unreliable and overconfident inference; this phenomenon can be partially mitigated by performing a Robustness Analysis of the model predictions to changes in the parameters. In this work, we address the problem of assessing the robustness of MAP inferences produced with Selective SPNs to global perturbations of the parameters. We present efficient algorithms and an empirical analysis with realistic problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-villanueva-llerena19a, title = {Robust Analysis of MAP Inference in Selective Sum-Product Networks}, author = {Villanueva Llerena, Julissa Giuliana and Mau\'{a}, Denis Deratani}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {430--440}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/villanueva-llerena19a/villanueva-llerena19a.pdf}, url = {https://proceedings.mlr.press/v103/villanueva-llerena19a.html}, abstract = {Sum-Product Networks (SPN) are deep probabilistic models that have shown to achieve state-of-the-art performance in several machine learning tasks. As with many other probabilistic models, performing Maximum-A-Posteriori (MAP) inference is NP-hard in SPNs. A notable exception is selective SPNs, that constrain the network so as to allow MAP inference to be performed in linear time. Due to the high number of parameters, SPNs learned from data can produce unreliable and overconfident inference; this phenomenon can be partially mitigated by performing a Robustness Analysis of the model predictions to changes in the parameters. In this work, we address the problem of assessing the robustness of MAP inferences produced with Selective SPNs to global perturbations of the parameters. We present efficient algorithms and an empirical analysis with realistic problems.} }
Endnote
%0 Conference Paper %T Robust Analysis of MAP Inference in Selective Sum-Product Networks %A Julissa Giuliana Villanueva Llerena %A Denis Deratani Mauá %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-villanueva-llerena19a %I PMLR %P 430--440 %U https://proceedings.mlr.press/v103/villanueva-llerena19a.html %V 103 %X Sum-Product Networks (SPN) are deep probabilistic models that have shown to achieve state-of-the-art performance in several machine learning tasks. As with many other probabilistic models, performing Maximum-A-Posteriori (MAP) inference is NP-hard in SPNs. A notable exception is selective SPNs, that constrain the network so as to allow MAP inference to be performed in linear time. Due to the high number of parameters, SPNs learned from data can produce unreliable and overconfident inference; this phenomenon can be partially mitigated by performing a Robustness Analysis of the model predictions to changes in the parameters. In this work, we address the problem of assessing the robustness of MAP inferences produced with Selective SPNs to global perturbations of the parameters. We present efficient algorithms and an empirical analysis with realistic problems.
APA
Villanueva Llerena, J.G. & Mauá, D.D.. (2019). Robust Analysis of MAP Inference in Selective Sum-Product Networks. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:430-440 Available from https://proceedings.mlr.press/v103/villanueva-llerena19a.html.

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