Discriminative classification with generative features: bridging Naive Bayes and logistic regression
This is an incremental improvement for machine learning practitioners, offering a hybrid approach to enhance classification performance by combining generative and discriminative modeling.
The authors tackled the problem of bridging generative and discriminative classification by introducing Smart Bayes, a framework that integrates generative features into a discriminative classifier, resulting in performance that often outperforms both logistic regression and Naive Bayes in simulations and real-data studies.
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.