Balanced Product of Experts for Long-Tailed Recognition

Many real-world recognition problems suffer from an imbalanced or long-tailed label distribution. Those distributions make representation learning more 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. To this aim, recent works have extended softmax cross-entropy using margin modifications, inspired by Bayes' theorem. In this paper, we generalize several approaches with a Balanced Product of Experts (BalPoE), which combines a family of models with different test-time target distributions to tackle the imbalance in the data. The proposed experts are trained in a single stage, either jointly or independently, and fused seamlessly into a BalPoE. We show that BalPoE is Fisher consistent for minimizing the balanced error and perform extensive experiments to validate the effectiveness of our approach. Finally, we investigate the effect of Mixup in this setting, discovering that regularization is a key ingredient for learning calibrated experts. Our experiments show that a regularized BalPoE can perform remarkably well in test accuracy and calibration metrics, leading to state-of-the-art results on CIFAR-100-LT, ImageNet-LT, and iNaturalist-2018 datasets. The code will be made publicly available upon paper acceptance.