Discriminative classification with generative features: bridging Naive Bayes and logistic regression

TL;DR

Smart Bayes is a hybrid classification method that combines generative density ratios with discriminative logistic regression, improving accuracy by leveraging the strengths of both approaches.

Contribution

It introduces a novel framework that integrates likelihood-ratio features into discriminative classifiers, with a flexible spline-based estimator for density ratios.

Findings

Smart Bayes often outperforms logistic regression and Naive Bayes in experiments.

The method provides stronger class separation than raw covariates.

Hybrid generative-discriminative approaches can enhance classification performance.

Abstract

We introduce Smart Bayes, a new classification framework that bridges generative and discriminative modeling by integrating likelihood-ratio-based generative features into a logistic-regression-style discriminative classifier. From the generative perspective, Smart Bayes relaxes the fixed unit weights of Naive Bayes by allowing data-driven coefficients on density-ratio features. From a discriminative perspective, it constructs transformed inputs as marginal log-density ratios that explicitly quantify how much more likely each feature value is under one class than another, thereby providing predictors with stronger class separation than the raw covariates. To support this framework, we develop a spline-based estimator for univariate log-density ratios that is flexible, robust, and computationally efficient. Through extensive simulations and real-data studies, Smart Bayes often outperforms both logistic regression and Naive Bayes. Our results highlight the potential of hybrid approaches that exploit generative structure to enhance discriminative performance.