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We propose a high dimensional classification method that involvesnonparametric feature augmentation. Knowing that marginal density ratios arethe most powerful univariate classifiers, we use the ratio estimates totransform the original feature measurements. Subsequently, penalized logisticregression is invoked, taking as input the newly transformed or augmentedfeatures. This procedure trains models equipped with local complexity andglobal simplicity, thereby avoiding the curse of dimensionality while creatinga flexible nonlinear decision boundary. The resulting method is called FeatureAugmentation via Nonparametrics and Selection (FANS). We motivate FANS bygeneralizing the Naive Bayes model, writing the log ratio of joint densities asa linear combination of those of marginal densities. It is related togeneralized additive models, but has better interpretability and computability.Risk bounds are developed for FANS. In numerical analysis, FANS is comparedwith competing methods, so as to provide a guideline on its best applicationdomain. Real data analysis demonstrates that FANS performs very competitivelyon benchmark email spam and gene expression data sets. Moreover, FANS isimplemented by an extremely fast algorithm through parallel computing.

Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification