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Naïve Bayes learners are widely used, efficient, and effective supervised learning methods for labeled datasets in noisy environments. It has been shown that naïve Bayes learners produce reasonable performance compared with other machine learning algorithms. However, the conditional independence assumption of naïve Bayes learning imposes restrictions on the handling of real-world data. To relax the independence assumption, we propose a smooth kernel to augment weights for the likelihood estimation. We then select an attribute weighting method that uses the mutual information metric to cooperate with the proposed framework. A series of experiments are conducted on 17 UCI benchmark datasets to compare the accuracy of the proposed learner against that of other methods that employ a relaxed conditional independence assumption. The results demonstrate the effectiveness and efficiency of our proposed learning algorithm. The overall results also indicate the superiority of attribute-weighting methods over those that attempt to determine the structure of the network.

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Naive Bayes (NB) learning is more popular, faster and effective supervised learning method to handle the labeled datasets especially in which have some noises, NB learning also has well performance. However, the conditional independent assumption of NB learning imposes some restriction on the property of handling data of real world. Some researchers proposed lots of methods to relax NB assumption, those methods also include attribute weighting, kernel density estimating. In this paper, we propose a novel approach called NB Based on Attribute Weighting in Kernel Density Estimation (NBAWKDE) to improve the NB learning classification ability via combining kernel density estimation and attribute weighting based on conditional mutual information. Our method makes the weights embedded in kernel have the relatively interpretable meaning, it is flexible that we also can choice different metrics and methods to measure the weights based on our attribute weighting in kernel density estimation framework.

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