Selective regression allows abstention from prediction if the confidence to make an accurate prediction is not sufficient. In general, by allowing a reject option, one expects the performance of a regression model to increase at the cost of reducing coverage (i.e., by predicting fewer samples). However, as shown in this work, in some cases, the performance of minority group can decrease while we reduce the coverage, and thus selective regression can magnify disparities between different sensitive groups. We show that such an unwanted behavior can be avoided if we can construct features satisfying the sufficiency criterion, so that the mean prediction and the associated uncertainty are calibrated across all the groups. Further, to mitigate the disparity in the performance across groups, we introduce two approaches based on this calibration criterion: (a) by regularizing an upper bound of conditional mutual information under a Gaussian assumption and (b) by regularizing a contrastive loss for mean and uncertainty prediction. The effectiveness of these approaches are demonstrated on synthetic as well as real-world datasets.
翻译:选择性回归使得人们可以放弃预测,如果对准确预测的信心不够充分的话。 一般来说,如果允许拒绝选项,人们期望回归模型的性能会以降低覆盖率(即通过预测较少的样本)为代价而增加。 但是,正如这项工作所显示的那样,在某些情况下,少数群体的性能会下降,而我们则会缩小覆盖面,因此选择性回归会扩大不同敏感群体之间的差别。我们表明,如果我们能够建立符合充足性标准的特征,从而对所有群体进行平均预测和相关的不确定性校准,那么这种不想要的行为是可以避免的。此外,为了缩小不同群体之间业绩的差异,我们根据这一校准标准采用了两种方法:(a) 将高斯假设下的附带条件的相互信息的上限定期化,以及(b) 将中度和不确定性预测的对比性损失定期化。这些方法的有效性既体现在合成数据上,也体现在真实世界的数据集上。