We address imbalanced classification, the problem in which a label may have
low marginal probability relative to other labels, by weighting losses
according to the correct class. First, we examine the convergence rates of the
expected excess weighted risk of plug-in classifiers where the weighting for
the plug-in classifier and the risk may be different. This leads to irreducible
errors that do not converge to the weighted Bayes risk, which motivates our
consideration of robust risks. We define a robust risk that minimizes risk over
a set of weightings and show excess risk bounds for this problem. Finally, we
show that particular choices of the weighting set leads to a special instance
of conditional value at risk (CVaR) from stochastic programming, which we call
label conditional value at risk (LCVaR). Additionally, we generalize this
weighting to derive a new robust risk problem that we call label heterogeneous
conditional value at risk (LHCVaR). Finally, we empirically demonstrate the
efficacy of LCVaR and LHCVaR on improving class conditional risks.

本研究提出了一种针对不平衡分类问题的解决方案，使用加权损失按照正确分类对错误分类的影响程度进行损失估计，进而提出了鲁棒风险的概念，得出了特殊情况下的条件价值风险的鲁棒风险解法，同时这种解法可用于改善类条件风险。