Bayes’ theorem tells us how to optimally predict the class of a previously unseen example, given a training sample. The chosen class should be the one which maximizes P(CilE) = P(Ci) P(EICi) /P(E), where Ci is the ith class, E is the test example, P(YIX) denotes the conditional probability of Y given X, and probabilities are estimated from the training sample. Let an example be a vector of a at...

Naive Bayesian classi ers utilise a simple mathematical model for induction. While it is known that the assumptions on which this model is based are frequently violated, the predictive accuracy obtained in discriminate classi cation tasks is surprisingly competitive in comparison to more complex induction techniques. Adjusted probability naive Bayesian induction adds a simple extension to the n...

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A novel Bayesian classifier with smaller eigenvalues reset by threshold based on database is proposed in this paper. The threshold is used to substitute eigenvalues of scatter matrices which are smaller than the threshold to minimize the classification error rate with a given database, thus improving the performance of Bayesian classifier. Several experiments have shown its effectiveness. The e...

The simple Bayesian classiier (SBC), sometimes called Naive-Bayes, is built based on a conditional independence model of each attribute given the class. The model was previously shown to be surprisingly robust to obvious violations of this independence assumption, yielding accurate classiication models even when there are clear conditional dependencies. The SBC can serve as an excellent tool fo...

Neyman-Pearson or frequentist inference and Bayes inference are most clearly differentiated by their approaches to point null hypothesis testing. With very large samples, the frequentist and Bayesian conclusions from a classical test of significance for a point null hypothesis can be contradictory, with a small frequentist P -value casting serious doubt on the null hypothesis, but a large Bayes...

This paper proposes a new approach based on augmented naive Bayes for image classification. Initially, each image is cutting in a whole of blocks. For each block, we compute a vector of descriptors. Then, we propose to carry out a classification of the vectors of descriptors to build a vector of labels for each image. Finally, we propose three variants of Bayesian Networks such as Naïve Bayesia...

Bayesian Classifiers Learn joint distribution P(C,F) Assign to f the most probable class label argmaxc′∈C P(c′, f̃) This defines a classifier, i.e., a map: (F1× . . .×Fm)→ C Credal Classifiers Learn joint credal set P(C,F) Set of optimal classes (e.g., according to maximality ) {c′ ∈ C |@c′′ ∈ C ,∀P ∈ P : P(c′′|f̃) > P(c′|f̃)} This defines a credal classifier, i.e., (F1× . . .×Fm)→ 2 May return mo...

The generalized Dirichlet distribution has been shown to be a more appropriate prior for naı̈ve Bayesian classifiers, because it can release both the negative-correlation and the equal-confidence requirements of the Dirichlet distribution. The previous research did not take the impact of individual attributes on classification accuracy into account, and therefore assumed that all attributes foll...

This study provides operational guidance for using naïve Bayes Bayesian network (BN) models in bankruptcy prediction. First, we suggest a heuristic method that guides the selection of bankruptcy predictors from a pool of potential variables. The method is based upon the assumption that the joint distribution of the variables is multivariate normal. Variables are selected based upon correlations...