On Discriminative Bayesian Network Classifiers and Logistic Regression

On Discriminative Bayesian Network Classifiers and Logistic Regression (2005)

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by Teemu Roos , Hannes Wettig , Peter Grünwald , Petri Myllymäki , Henry Tirri , Pedro Larrañaga , Jose A. Lozano , Jose M. Peña , Iñaki Inza

Venue:	Machine Learning
Citations:	11 - 1 self

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Datum	Value	Source
TITLE	On Discriminative Bayesian Network Classifiers and Logistic Regression	user correction - Legacy Corrections
AUTHOR NAME	Teemu Roos	user correction - Legacy Corrections
AUTHOR AFFIL	HANNES WETTIG; Complex Systems Computation Group, Helsinki Institute for Information Technology	user correction - Legacy Corrections
AUTHOR ADDR	P.O. Box 9800,; FI-02015 TKK, Finland	user correction - Legacy Corrections
AUTHOR NAME	Hannes Wettig	user correction - Legacy Corrections
AUTHOR NAME	Peter Grünwald	user correction - Legacy Corrections
AUTHOR ADDR	Centrum voor Wiskunde en Informatica, P.O. Box 94079, NL-1090 GB Amsterdam, The Netherlands	user correction - Legacy Corrections
AUTHOR NAME	Petri Myllymäki	user correction - Legacy Corrections
AUTHOR AFFIL	Complex Systems Computation Group, Helsinki Institute for Information Technology, P.O. Box 9800,	user correction - Legacy Corrections
AUTHOR ADDR	FI-02015 TKK, Finland	user correction - Legacy Corrections
AUTHOR NAME	Henry Tirri	user correction - Legacy Corrections
AUTHOR AFFIL	Complex Systems Computation Group, Helsinki Institute for Information Technology, P.O. Box 9800,	user correction - Legacy Corrections
AUTHOR ADDR	FI-02015 TKK, Finland	user correction - Legacy Corrections
AUTHOR NAME	Pedro Larrañaga	user correction - Legacy Corrections
AUTHOR NAME	Jose A. Lozano	user correction - Legacy Corrections
AUTHOR NAME	Jose M. Peña	user correction - Legacy Corrections
AUTHOR NAME	Iñaki Inza	user correction - Legacy Corrections
ABSTRACT	Discriminative learning of the parameters in the naive Bayes model is known to be equivalent to a logistic regression problem. Here we show that the same fact holds for much more general Bayesian network models, as long as the corresponding network structure satisfies a certain graph-theoretic property. The property holds for naive Bayes but also for more complex structures such as tree-augmented naive Bayes (TAN) as well as for mixed diagnostic-discriminative structures. Our results imply that for networks satisfying our property, the conditional likelihood cannot have local maxima so that the global maximum can be found by simple local optimization methods. We also show that if this property does not hold, then in general the conditional likelihood can have local, non-global maxima. We illustrate our theoretical results by empirical experiments with local optimization in a conditional naive Bayes model. Furthermore, we provide a heuristic strategy for pruning the number of parameters and relevant features in such models. For many data sets, we obtain good results with heavily pruned submodels containing many fewer parameters than the original naive Bayes model.	user correction - Legacy Corrections
YEAR	2005	INFERENCE
VENUE	Machine Learning	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	267--296	INFERENCE
VOLUME	59	INFERENCE
CITATIONS	40 found	ParsCit 1.0