We introduce a general iterative procedure called risk-based calibration (RC) designed to minimize the empirical risk under the 0-1 loss (empirical error) for probabilistic classifiers. These classifiers are based on modeling probability distributions, including those constructed from the joint distribution (generative) and those based on the class conditional distribution (conditional). RC can be particularized to any probabilistic classifier provided a specific learning algorithm that computes the classifier's parameters in closed form using data statistics. RC reinforces the statistics aligned with the true class while penalizing those associated with other classes, guided by the 0-1 loss. The proposed method has been empirically tested on 30 datasets using na\"ive Bayes, quadratic discriminant analysis, and logistic regression classifiers. RC improves the empirical error of the original closed-form learning algorithms and, more notably, consistently outperforms the gradient descent approach with the three classifiers.

本研究针对概率分类器的经验风险（0-1损失）进行了校准，填补了由于模型概率分布引发的性能差距。提出的基于风险的校准方法（RC）通过优化学习算法来调整分类器参数，显著降低了经验错误，尤其是在使用朴素贝叶斯、二次判别分析和逻辑回归的测试中，其表现优于梯度下降法。

基于风险的概率分类器校准