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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 and

can be used to estimate joint density ratios. We then use the spline method to construct

a new classifier named DAB, or Dependence-Adjusted naive Bayes. The DAB classifier

estimates 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 certain

Gaussian situations where naive Bayes cannot, and we also demonstrate its performance

on simulated and empirical datasets. We also recreate a comparison of naive Bayes and

logistic regression from Ng and Jordan (Ng and Jordan, 2002) and show where DAB can outperform both

methods. Last, we demonstrate DAB’s effectiveness in the setting of functional data as

an extension to the functional naive Bayes classifier (Dai, Mueller, and Yao, 2017).

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