Bayesian Networks (BNs) have received significant attention in various academic and industrial applications, such as modeling knowledge in image processing, engineering, medicine and bio-informatics. Preserving the privacy of sensitive data, owned by different parties, is often a critical issue. However, in many practical applications, BNs must train from data that gradually becomes available at different period of times, on which the traditional batch learning algorithms are not suitable or applicable. In this paper, an algorithm based on a new and efficient version of Sufficient Statistics is proposed for incremental learning with BNs. The standard K2 algorithm is also modified to be utilized inside the incremental learning algorithm. Next, some secure building blocks such as secure comparison, and factorial, which are resistant against colluding attacks and could be applied securely over public channels like internet, are presented to be used inside the main protocol. Then a privacy-preserving protocol is proposed for incremental learning of BNs, in which the structure and probabilities are estimated incrementally from homogeneously distributed and gradually available data among two or multi-parties. Finally, security and complexity analysis along with the experimental results are presented to compare with the batch algorithm and to show its performance and applicability in real world applications. ?? 2013 Elsevier B.V.
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