TY - JOUR
T1 - A Pairwise Naïve Bayes Approach to Bayesian Classification
AU - Asafu-Adjei, Josephine K.
AU - Betensky, Rebecca A.
N1 - Funding Information:
The authors thank BG Medicine, Inc. for providing the cardiovascular biomarker data, Drs. Xingbin Wang (Department Human Genetics, University of Pittsburgh Graduate School of Public Health, Pittsburgh, PA) and Etienne Sibille (Department of Psychiatry, University of Pittsburgh, Pittsburgh, PA) for providing the genetic microarray data, and Dr. William H. Wolberg (University of Wisconsin Hospital, Madison, WI) for providing the \bcw" data set. The authors also thank the Editor, Associate Editor, and reviewers of International Journal of Pattern Recognition and Arti¯cial Intelligence and Machine Learning for their helpful suggestions, which improved our presentation. This work was supported by the National Institutes of Health [T32NS048005 to J.K.A. and R.A.B.; F32NS081904 to J.K.A.]. The content
Publisher Copyright:
© 2015 World Scientific Publishing Company.
PY - 2015/11/30
Y1 - 2015/11/30
N2 - Despite the relatively high accuracy of the naïve Bayes (NB) classifier, there may be several instances where it is not optimal, i.e. does not have the same classification performance as the Bayes classifier utilizing the joint distribution of the examined attributes. However, the Bayes classifier can be computationally intractable due to its required knowledge of the joint distribution. Therefore, we introduce a "pairwise naïve" Bayes (PNB) classifier that incorporates all pairwise relationships among the examined attributes, but does not require specification of the joint distribution. In this paper, we first describe the necessary and sufficient conditions under which the PNB classifier is optimal. We then discuss sufficient conditions for which the PNB classifier, and not NB, is optimal for normal attributes. Through simulation and actual studies, we evaluate the performance of our proposed classifier relative to the Bayes and NB classifiers, along with the HNB, AODE, LBR and TAN classifiers, using normal density and empirical estimation methods. Our applications show that the PNB classifier using normal density estimation yields the highest accuracy for data sets containing continuous attributes. We conclude that it offers a useful compromise between the Bayes and NB classifiers.
AB - Despite the relatively high accuracy of the naïve Bayes (NB) classifier, there may be several instances where it is not optimal, i.e. does not have the same classification performance as the Bayes classifier utilizing the joint distribution of the examined attributes. However, the Bayes classifier can be computationally intractable due to its required knowledge of the joint distribution. Therefore, we introduce a "pairwise naïve" Bayes (PNB) classifier that incorporates all pairwise relationships among the examined attributes, but does not require specification of the joint distribution. In this paper, we first describe the necessary and sufficient conditions under which the PNB classifier is optimal. We then discuss sufficient conditions for which the PNB classifier, and not NB, is optimal for normal attributes. Through simulation and actual studies, we evaluate the performance of our proposed classifier relative to the Bayes and NB classifiers, along with the HNB, AODE, LBR and TAN classifiers, using normal density and empirical estimation methods. Our applications show that the PNB classifier using normal density estimation yields the highest accuracy for data sets containing continuous attributes. We conclude that it offers a useful compromise between the Bayes and NB classifiers.
KW - Bayesian classification
KW - naïve Bayes classifier
KW - optimal classification
KW - pairwise naïve Bayes classifier
KW - semi-naïve Bayes classifier
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U2 - 10.1142/S0218001415500238
DO - 10.1142/S0218001415500238
M3 - Article
AN - SCOPUS:84942826208
SN - 0218-0014
VL - 29
JO - International Journal of Pattern Recognition and Artificial Intelligence
JF - International Journal of Pattern Recognition and Artificial Intelligence
IS - 7
M1 - 1550023
ER -