Joint Distribution Estimation and Naïve Bayes Classification Under Local Differential Privacy

Abstract

Naïve Bayes classifier (NBC) is a fundamental and widely-used data mining tool. To respond to the growing privacy concern, several privacy-preserving NBC schemes have been proposed recently. Generally, the existing schemes mainly exploit two different techniques: one is secure multi-party computation (SMCP); and the other is (local) differential privacy (DP/LDP). However, the approaches with SMCP would employ some encryption algorithms, which results in heavy computation and communication costs and impedes the usage of the approaches in practice. The existing methods with DP/LDP also have some deficiencies. For instance, a trusted data curator is required or the class labels of individuals are revealed. To make up the drawbacks of previous schemes, in this article, we develop a novel scheme to train a Naïve Bayes classifier with privacy guarantee in the local setting. We first design a method (JESS) for joint distribution estimation under LDP. Then we apply JESS to calculate the conditional probability, the key of the Naïve Bayes classification and train a Naïve Bayes classifier. Additionally, we leverage extensive experiments to evaluate the effectiveness of our schemes designed for joint distribution and Naïve Bayes classification. Compared with the existing schemes, ours can achieve higher accuracy.