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.

This paper proposes an approach to automatically categorize the social interactions of a user wearing a photo-camera (2fpm), by relying solely on what the camera is seeing. The problem is challenging due to the overwhelming complexity of social life and the extreme intra-class variability of social interactions captured under unconstrained conditions. We adopt the formalization proposed in Bugental's social theory, that groups human relations into five social domains with related categories. Our method is a new deep learning architecture that exploits the hierarchical structure of the label space and relies on a set of social attributes estimated at frame level to provide a semantic representation of social interactions. Experimental results on the new EgoSocialRelation dataset demonstrate the effectiveness of our proposal.