代价敏感学习中的损失函数设计

Design of loss function for cost-sensitive learning

一般的学习算法通过最小化分类损失使分类错误率最小化,而代价敏感学习则以最小化分类代价为目标,需构造代价敏感损失.本文探讨代价敏感损失的设计准则,首先介绍基于代价敏感风险优化的代价敏感学习方法,然后在Bayes最优分类理论框架下,提出两条代价敏感损失设计准则.接着采用两种常用代价敏感损失生成方法构造平方损失、指数损失、对数损失、支持向量机损失等经典损失函数的代价敏感扩展形式.根据所提出的设计准则,从理论上分析这些代价敏感损失的性能.最后通过实验表明,同时满足两条设计准则的代价敏感损失能有效降低分类代价,从而证明了本文提出的代价敏感损失设计准则的合理性.

Conventional learning algorithms minimize the classification error through minimizing the classification loss. However, the cost-sensitive learning minimizes the classification cost; thus, cost-sensitive losses have to be constructed. This paper studies the design criteria for cost-sensitive loss functions. Firstly, cost-sensitive learning methods based on cost-sensitive risk minimization are briefly introduced. Then, under the theory framework of Bayes optimal classification, two design guidelines of cost-sensitive loss function are proposed. The cost-sensitive extensions of several classic loss functions （e.g., square loss, exponential loss, log loss and support vector machine （SVM） loss） are generated via two most popular construction methods of cost-sensitive loss. The performances of these cost-sensitive losses are theoretically analyzed based on the proposed two design guidelines. Experimental results have shown that those cost-sensitive losses that satisfy both of the two design criteria significantly reduce classification costs, demonstrating the rationality of the proposed design criteria of cost-sensitive loss.