On the Asymptotic Optimality of Maximum Margin Bayesian Networks

Sebastian Tschiatschek, Franz Pernkopf
Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, PMLR 31:590-598, 2013.

Abstract

Maximum margin Bayesian networks (MMBNs) are Bayesian networks with discriminatively optimized parameters. They have shown good classification performance in various applications. However, there has not been any theoretic analysis of their asymptotic performance, e.g. their Bayes consistency. For specific classes of MMBNs, i.e. MMBNs with fully connected graphs and discrete-valued nodes, we show Bayes consistency for binary-class problems and a sufficient condition for Bayes consistency in the multi-class case. We provide simple examples showing that MMBNs in their current formulation are not Bayes consistent in general. These examples are especially interesting, as the model used for the MMBNs can represent the assumed true distributions. This indicates that the current formulations of MMBNs may be deficient. Furthermore, experimental results on the generalization performance are presented.

Cite this Paper

BibTeX
@InProceedings{pmlr-v31-tschiatschek13a, title = {On the Asymptotic Optimality of Maximum Margin Bayesian Networks}, author = {Tschiatschek, Sebastian and Pernkopf, Franz}, booktitle = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics}, pages = {590--598}, year = {2013}, editor = {Carvalho, Carlos M. and Ravikumar, Pradeep}, volume = {31}, series = {Proceedings of Machine Learning Research}, address = {Scottsdale, Arizona, USA}, month = {29 Apr--01 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v31/tschiatschek13a.pdf}, url = {https://proceedings.mlr.press/v31/tschiatschek13a.html}, abstract = {Maximum margin Bayesian networks (MMBNs) are Bayesian networks with discriminatively optimized parameters. They have shown good classification performance in various applications. However, there has not been any theoretic analysis of their asymptotic performance, e.g. their Bayes consistency. For specific classes of MMBNs, i.e. MMBNs with fully connected graphs and discrete-valued nodes, we show Bayes consistency for binary-class problems and a sufficient condition for Bayes consistency in the multi-class case. We provide simple examples showing that MMBNs in their current formulation are not Bayes consistent in general. These examples are especially interesting, as the model used for the MMBNs can represent the assumed true distributions. This indicates that the current formulations of MMBNs may be deficient. Furthermore, experimental results on the generalization performance are presented.} }
Endnote
%0 Conference Paper %T On the Asymptotic Optimality of Maximum Margin Bayesian Networks %A Sebastian Tschiatschek %A Franz Pernkopf %B Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2013 %E Carlos M. Carvalho %E Pradeep Ravikumar %F pmlr-v31-tschiatschek13a %I PMLR %P 590--598 %U https://proceedings.mlr.press/v31/tschiatschek13a.html %V 31 %X Maximum margin Bayesian networks (MMBNs) are Bayesian networks with discriminatively optimized parameters. They have shown good classification performance in various applications. However, there has not been any theoretic analysis of their asymptotic performance, e.g. their Bayes consistency. For specific classes of MMBNs, i.e. MMBNs with fully connected graphs and discrete-valued nodes, we show Bayes consistency for binary-class problems and a sufficient condition for Bayes consistency in the multi-class case. We provide simple examples showing that MMBNs in their current formulation are not Bayes consistent in general. These examples are especially interesting, as the model used for the MMBNs can represent the assumed true distributions. This indicates that the current formulations of MMBNs may be deficient. Furthermore, experimental results on the generalization performance are presented.
RIS
TY - CPAPER TI - On the Asymptotic Optimality of Maximum Margin Bayesian Networks AU - Sebastian Tschiatschek AU - Franz Pernkopf BT - Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics DA - 2013/04/29 ED - Carlos M. Carvalho ED - Pradeep Ravikumar ID - pmlr-v31-tschiatschek13a PB - PMLR DP - Proceedings of Machine Learning Research VL - 31 SP - 590 EP - 598 L1 - http://proceedings.mlr.press/v31/tschiatschek13a.pdf UR - https://proceedings.mlr.press/v31/tschiatschek13a.html AB - Maximum margin Bayesian networks (MMBNs) are Bayesian networks with discriminatively optimized parameters. They have shown good classification performance in various applications. However, there has not been any theoretic analysis of their asymptotic performance, e.g. their Bayes consistency. For specific classes of MMBNs, i.e. MMBNs with fully connected graphs and discrete-valued nodes, we show Bayes consistency for binary-class problems and a sufficient condition for Bayes consistency in the multi-class case. We provide simple examples showing that MMBNs in their current formulation are not Bayes consistent in general. These examples are especially interesting, as the model used for the MMBNs can represent the assumed true distributions. This indicates that the current formulations of MMBNs may be deficient. Furthermore, experimental results on the generalization performance are presented. ER -
APA
Tschiatschek, S. & Pernkopf, F.. (2013). On the Asymptotic Optimality of Maximum Margin Bayesian Networks. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 31:590-598 Available from https://proceedings.mlr.press/v31/tschiatschek13a.html.

Related Material