用生成模型特征增强逻辑回归，提升分类效果
Discriminative classification with generative features: bridging Naive Bayes and logistic regression
- 将密度比特征融入逻辑回归，动态学习权重
- 在多个数据集上优于朴素贝叶斯和逻辑回归
- 适合希望结合生成与判别优势的研究者
我们提出 Smart Bayes，一种融合生成与判别建模的新分类框架。该方法将基于似然比的生成特征引入逻辑回归式判别分类器中。从生成视角看，Smart Bayes 放松了朴素贝叶斯固定的单位权重，允许通过数据驱动方式学习密度比特征的系数。从判别视角看，它将输入转换为边际对数密度比，明确量化每个特征值在某一类别下比另一类别更可能出现的程度，从而提供比原始协变量更强的类别区分能力。为此，我们开发了一种基于样条的单变量对数密度比估计器，具有灵活性、鲁棒性和计算高效性。通过大量模拟和真实数据实验，Smart Bayes 常常优于逻辑回归和朴素贝叶斯。结果表明，利用生成结构来提升判别性能的混合方法具有巨大潜力。
原文摘要 · Abstract (English)
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.
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