Classification methods for multivariate and functional data using features from density ratio estimation
- Author(s): Terner, Zachary
- Advisor(s): Wang, Yuedong
- Petersen, Alexander
- et al.
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).