Supervised classification techniques use training samples to learn a classification rule with small expected 0-1 loss (error probability). Conventional methods enable tractable learning and provide out-of-sample generalization by using surrogate losses instead of the 0-1 loss and considering specific families of rules (hypothesis classes). This paper presents minimax risk classifiers (MRCs) that minimize the worst-case 0-1 loss over general classification rules and provide tight performance guarantees at learning. We show that MRCs are strongly universally consistent using feature mappings given by characteristic kernels. The paper also proposes efficient optimization techniques for MRC learning and shows that the methods presented can provide accurate classification together with tight performance guarantees in practice.
翻译:受监督的分类技术利用培训样本来学习一项分类规则,预期损失为0-1小(概率低); 常规方法能够进行可移植学习,通过使用代用损失而不是0-1损失和考虑特定规则类别(假肢类),提供全方位的概括性说明; 本文介绍了微型最大风险分类(MRC),这些分类将最差的零-1损失与一般分类规则相比降到最低,并在学习时提供严格的性能保障; 我们表明,利用特质内核提供的特征图谱,MRC具有很强的普遍一致性; 论文还提出了用于MRC学习的高效优化技术,并表明所提出的方法可以提供准确的分类,同时在实践中提供严格的性能保障。