Towards Calibrated Model for Long-Tailed Visual Recognition from Prior Perspective - Supplementary Material - Shenzhen International Graduate School, Tsinghua University

A.1 Basic setting Setting 1 Without loss of generality, we suppose that the long-tailed distribution satisfies some kind exponential distribution with parameter [8]. Proof A.1 Follow the Basic Setting 1, when mixing factor Beta(,), consider a -Aug sample generated by ex Therefore, the head gets more regulation than the tail. One the one hand, the classification performance will be promoted. On the other hand, however, the performance gap between the head and tail still exists. Hence we can generalize Eq.A.9 to: Z y According to Eq.A.11, it's easy to find a derivative zero point in range [1,C]. UniMix Factor (green) alleviates such situation and the full pipeline ( = 1) constructs a more uniform distribution of -Aug (red), which contributes to a well-calibrated model. As illustrated in Fig.A1, when the class number C and imbalance factor get larger, the limitations of mixup in LT scenarios gradually appear. It has limited contribution for the tail class' feature learning and regulation, which is the reason for its poor calibration.