  In machine learning, classification models need to be trained in order to
predict class labels. When the training data contains personal information
about individuals, collecting training data becomes difficult due to privacy
concerns. Local differential privacy is a definition to measure the individual
privacy when there is no trusted data curator. Individuals interact with an
untrusted data aggregator who obtains statistical information about the
population without learning personal data. In order to train a Naive Bayes
classifier in an untrusted setting, we propose to use methods satisfying local
differential privacy. Individuals send their perturbed inputs that keep the
relationship between the feature values and class labels. The data aggregator
estimates all probabilities needed by the Naive Bayes classifier. Then, new
instances can be classified based on the estimated probabilities. We propose
solutions for both discrete and continuous data. In order to eliminate high
amount of noise and decrease communication cost in multi-dimensional data, we
propose utilizing dimensionality reduction techniques which can be applied by
individuals before perturbing their inputs. Our experimental results show that
the accuracy of the Naive Bayes classifier is maintained even when the
individual privacy is guaranteed under local differential privacy, and that
using dimensionality reduction enhances the accuracy.
