Abstract. Predictive accuracy has been widely used as the main criterion for comparing the predictive ability of classification systems (such as C4.5, neural networks, and Naive Bayes). Most of these classifiers also produce probability estimations of the classification, but they are completely ignored in the accuracy measure. This is often taken for granted because both training and testing sets only provide class labels. In this paper we establish rigourously that, even in this setting, the area under the ROC (Receiver Operating Characteristics) curve, or simply AUC, provides a better measure than accuracy. Our result is quite significant for three reasons. First, we establish, for the first time, rigourous criteria for comparing evaluation measures for learning algorithms. Second, it suggests that AUC should replace accuracy when measuring and comparing classification systems. Third, our result also prompts us to re-evaluate many well-established conclusions based on accuracy in machine learning. For example, it is well accepted in the machine learning community that, in terms of predictive accuracy, Naive Bayes and decision trees are very similar. Using AUC, however, we show experimentally that Naive Bayes is significantly better than the decision-tree learning algorithms.

Naïve Bayes is one of the most efficient and effective inductive learning algorithms for machine learning and data mining. Its competitive performance in classification is surprising, because the conditional independence assumption on which it is based is rarely true in real-world applications. An open question is: what is the true reason for the surprisingly good performance of Naïve Bayes in classification? In this paper, we propose a novel explanation for the good classification performance of Naïve Bayes. We show that, essentially, dependence distribution plays a crucial role. Here dependence distribution means how the local dependence of an attribute distributes in each class, evenly or unevenly, and how the local dependences of all attributes work together, consistently (supporting a certain classification) or inconsistently (canceling each other out). Specifically, we show that no matter how strong the dependences among attributes are, Naïve Bayes can still be optimal if the dependences distribute evenly in classes, or if the dependences cancel each other out. We propose and prove a sufficient and necessary condition for the optimality of Naïve Bayes. Further, we investigate the optimality of Naïve Bayes under the Gaussian distribution. We present and prove a sufficient condition for the optimality of Naïve Bayes, in which the dependences among attributes exist. This provides evidence that dependences may cancel each other out. Our theoretic analysis can be used in designing learning algorithms. In fact, a major class of learning algorithms for Bayesian networks are conditional independence-based (or CI-based), which are essentially based on dependence. We design a dependence distribution-based algorithm by extending the ChowLiu algorithm, a widely used CI based algorithm. Our experiments show that the new algorithm outperforms the ChowLiu algorithm, which also provides empirical evidence to support our new explanation.

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Fluoxetine is effective and well tolerated in the prevention of PTSD relapse for up to 6 months.

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Bayesian network classifiers have been widely used for classification problems. Given a fixed Bayesian network structure, parameters learning can take two different approaches: generative and discriminative learning. While generative parameter learning is more efficient, discriminative parameter learning is more effective. In this paper, we propose a simple, efficient, and effective discriminative parameter learning method, called Discriminative Frequency Estimate (DFE), which learns parameters by discriminatively computing frequencies from data. Empirical studies show that the DFE algorithm integrates the advantages of both generative and discriminative learning: it performs as well as the state-of-the-art discriminative parameter learning method ELR in accuracy, but is significantly more efficient.

Abstract. It is well-known that naive Bayes performs surprisingly well in classification, but its probability estimation is poor. In many applications, however, a ranking based on class probabilities is desired. For example, a ranking of customers in terms of the likelihood that they buy one's products is useful in direct marketing. What is the general performance of naive Bayes in ranking? In this paper, we study it by both empirical experiments and theoretical analysis. Our experiments show that naive Bayes outperforms C4.4, the most state-of-the-art decisiontree algorithm for ranking. We study two example problems that have been used in analyzing the performance of naive Bayes in classification [3]. Surprisingly, naive Bayes performs perfectly on them in ranking, even though it does not in classification. Finally, we present and prove a sufficient condition for the optimality of naive Bayes in ranking.

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