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Asymptotic Properties of Maximum Collective Conditional Likelihood Estimators for Naïve Bayes Classifiers
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan.ORCID iD: 0000-0003-1654-9148
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan.
2006 (English)In: International Journal of Statistics and Systems, ISSN 0973-2675Article in journal (Refereed) Accepted
Abstract [en]

Bayesian networks that are probabilistic expert systems can be used as classifiers. Special type of Bayesian networks called naive Bayes classifiers are popular in practice due to their good performance although they are relatively simple.  

Enhancement of the performance of the naïve Bayes classifier is often done through various parameter learning methods where the usual method is the method of maximum likelihood estimation. Nevertheless, since the true target of interest of Bayes classifiers is estimation of the conditional probabilities, it is natural to learn their parameters by maximization of the collective conditional likelihoods. Therefore, recently there has been a growing interest in learning the parameters of the naïve Bayes classifiers through maximizing collective conditional likelihoods.

Strong consistency and asymptotic normality are two basic statistical properties which any decent estimator should have although they are primarily of theoretical nature. In this research, we prove the strong consistency and asymptotic normality of the maximum collective conditional estimators for naïve Bayes classifiers. Essentially our proof follows the classical ideas well-developed for the theory of maximum likelihood estimation.   

 

Place, publisher, year, edition, pages
India: Research India Publications , 2006.
Keyword [en]
Bayesian network, dependence, classification accuracy
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-128747OAI: oai:DiVA.org:umu-128747DiVA: diva2:1056332
Available from: 2016-12-14 Created: 2016-12-13 Last updated: 2017-02-08

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Wijayatunga, Priyantha
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