Classification methods for multivariate and functional data using features from density ratio estimation

We introduce a new method for estimating density ratios using splines, as a generalization of a method from Silverman (Silverman, 1978). This method applies to general domains andcan be used to estimate joint density ratios. We then use the spline method to constructa new classifier named DAB, or Dependence-Adjusted naive Bayes. The DAB classifierestimates marginal log density ratios and uses them as features in a binary classification problem. We show that DAB may recover the optimal Bayes solution in certainGaussian situations where naive Bayes cannot, and we also demonstrate its performanceon simulated and empirical datasets. We also recreate a comparison of naive Bayes andlogistic regression from Ng and Jordan (Ng and Jordan, 2002) and show where DAB can outperform bothmethods. Last, we demonstrate DAB’s effectiveness in the setting of functional data asan extension to the functional naive Bayes classifier (Dai, Mueller, and Yao, 2017)