Many real-world recognition problems are characterized by long-tailed label distributions. These distributions make representation learning highly challenging due to limited generalization over the tail classes. If the test distribution differs from the training distribution, e.g. uniform versus long-tailed, the problem of the distribution shift needs to be addressed. A recent line of work proposes learning multiple diverse experts to tackle this issue. Ensemble diversity is encouraged by various techniques, e.g. by specializing different experts in the head and the tail classes. In this work, we take an analytical approach and extend the notion of logit adjustment to ensembles to form a Balanced Product of Experts (BalPoE). BalPoE combines a family of experts with different test-time target distributions, generalizing several previous approaches. We show how to properly define these distributions and combine the experts in order to achieve unbiased predictions, by proving that the ensemble is Fisher-consistent for minimizing the balanced error. Our theoretical analysis shows that our balanced ensemble requires calibrated experts, which we achieve in practice using mixup. We conduct extensive experiments and our method obtains new state-of-the-art results on three long-tailed datasets: CIFAR-100-LT, ImageNet-LT, and iNaturalist-2018. Our code is available at https://github.com/emasa/BalPoE-CalibratedLT.

翻译：许多实际识别问题具有长尾标签分布特征。此类分布因尾部类别泛化能力受限而导致表征学习极具挑战性。当测试分布与训练分布不一致时（例如均匀分布与长尾分布），需解决分布偏移问题。近期研究提出通过学习多个多样化专家模型应对该挑战，并采用头部与尾部类别专用专家等不同技术促进集成多样性。本文采用分析性方法，将逻辑调整概念扩展至集成学习，构建平衡专家乘积模型（BalPoE）。BalPoE通过整合具有不同测试阶段目标分布的专家族，泛化了多种先前方法。我们通过证明该集成在最小化平衡误差时满足Fisher一致性，系统阐释了如何正确定义这些分布并进行专家组合以实现无偏预测。理论分析表明，平衡集成需要校准专家——我们在实践中通过混合数据增强（mixup）实现该特性。经广泛实验验证，本方法在CIFAR-100-LT、ImageNet-LT和iNaturalist-2018三个长尾数据集上均取得最新最优结果。代码开源地址：https://github.com/emasa/BalPoE-CalibratedLT。