On Decision Boundaries of Naïve Bayes in Continuous Domains

in Continuous Domains Tapio Elomaa and Juho Rousu Department of Computer S ien e, University of Helsinki, Finland {elomaa,rousu} s.helsinki.fi Abstra t. Naïve Bayesian lassi ers assume the onditional independen e of attribute values given the lass. Despite this in pra ti e often violated assumption, these simple lassi ers have been found e ient, e e tive, and robust to noise. Dis retization of ontinuous attributes in naïve Bayesian lassi ers has a hieved a lot of attention re ently. Continuous attributes need not ne essarily be dis retized, but it uni es their handling with nominal attributes and an lead to improved lassi er performan e. We show that optimal partitioning results from de ision tree learning arry over to Naïve Bayes as well. In parti ular, it sets de ision boundaries on borders of segments with equal lass frequen y distribution. An optimal univariate dis retization with respe t to the Naïve Bayes rule an be found in linear time but, unfortunately, optimal multivariate optimization is intra table. 1 Introdu tion The naïve Bayesian lassi er, or Naïve Bayes, is surprisingly e e tive in lassi ation tasks. Therefore, even if it does not belong to state-of-the-art methods, it plays an important role alongside de ision tree learning as standard baseline methods of indu tive algorithms. Naïve Bayesian lassi ers have been studied extensively over the years [18, 19, 7℄. Springer 2003; Le ture Notes in Arti ial Intelligen e 2838, pp. 144 155. N. Lavra£ et al. (eds.): Knowledge Dis overy in Databases: PKDD 2003 Pro . 7th European Conferen e, PKDD'03 (Cavtat-Dubrovnik, Croatia).