In this paper we present a new Bayesian net work model for classification that combines the naive Bayes (NB} classifier and the fi nite mixture (FM} classifier. The resulting classifier aims at relaxing the strong assump tions on which the two component models are based, in an attempt to improve on their classification performance, both in terms of accuracy and in terms of calibration of the estimated probabilities. The proposed clas sifier is obtained by superimposing a finite mixture model on the set of feature variables of a naive Bayes modeL We present exper imental results that compare the predictive performance on real datasets of the new clas sifier with the predictive performance of the NB classifier and the FM classifier. be appropriate for classification purposes, and show that in many cases it may result in a model with worse predictive performance than the NB classifier. These results can be intuitively understood by noting that learning a BN model for classification corresponds to solving a harder problem than the one we need to solve, namely, the modeling of the joint probability distribu tion of all the domain variables, rather than the model ing of the conditional distribution of a particular class variable given a set of feature variables. Part of the reason for the NB model's resilience is in the choice of the measure adopted to assess its perfor mance, namely the classification accumcy or zero-one loss, defined as the proportion of cases correctly clas sified by the model (usually measured over a test-set, or cross-validated}. Recent results [9, 16] show that a classifier can achieve high classification accuracy even when its probability estimates are poorly calibrated.1 In a decision-theoretic framework, the probability es timates output by the model are necessary to compute the expected misclassification cost, (i.e., the expected utility) based on which the decision maker would se lect the optimal classification. Poorly calibrated prob ability estimates may lead to sub-optimal decisions. This is not a problem when the misclassification cost (or utility function) is known and fixed. However, in many circumstances, the misclassification cost is un known or unequal, that is, case-dependent.2 In these circumstances, the calibration of the classifier's proba bility estimates can be as important as its classification accuracy for the assessment of its performance. In this paper, we provide additional evidence that the NB model is poorly calibrated, and we present a new Bayesian network model for classification that com1The probability p of a given classification outcome c is considered perfectly calibrated when cases assigned a prob ability p of yielding outcome c, actually yield that outcome a fraction p of the time. 2Typical classification problems with unequal misclassi fication costs are fraud detection [12] and computer-aided medical diagnosis.
To give two examples, Monti and Cooper REF combine finite mixture model with naive Bayes classifier.
A Bayesian Network Classifier that Combines a Finite Mixture Model and a Naive Bayes Model
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Mathematics Computer Science