Naive Bayes classifiers boosted by sufficient dimension reduction: applications to top-k classification

The naive Bayes classifier is one of the most straightforward classification tools and directly estimates the class probability. However, because it relies on the independent assumption of the predictor, which is rarely satisfied in real-world problems, its application is limited in practice. In this article, we propose employing sufficient dimension reduction (SDR) to substantially improve the performance of the naive Bayes classifier, which is often deteriorated when the number of predictors is not restrictively small. This is not surprising as SDR reduces the predictor dimension without sacrificing classification information, and predictors in the reduced space are constructed to be uncorrelated. Therefore, SDR leads the naive Bayes to no longer be naive. We applied the proposed naive Bayes classifier after SDR to build a recommendation system for the eyewear-frames based on customers' face shape, demonstrating its utility in the top-k classification problem.