With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula @math , where @math is the number of samples and @math is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.
Our theoretical framework is inspired by the random covering problem @cite_56 , where the goal is to cover a large set by a sequence of i.i.d. random small sets. We simplify the problem in by making reasonable assumptions. Note that the effective number of samples proposed in this paper is different from the concept of effective sample size in statistics. The effective sample size is used to calculate variance when samples are correlated.
@cite_56
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An instance of a random constraint satisfaction problem defines a random subset 𝒮 (the set of solutions) of a large product space X N (the set of assignments). We consider two prototypical problem ensembles (random k -satisfiability and q -coloring of random regular graphs) and study the uniform measure with support on S . As the number of constraints per variable increases, this measure first decomposes into an exponential number of pure states (“clusters”) and subsequently condensates over the largest such states. Above the condensation point, the mass carried by the n largest states follows a Poisson-Dirichlet process. For typical large instances, the two transitions are sharp. We determine their precise location. Further, we provide a formal definition of each phase transition in terms of different notions of correlation between distinct variables in the problem. The degree of correlation naturally affects the performances of many search sampling algorithms. Empirical evidence suggests that local Monte Carlo Markov chain strategies are effective up to the clustering phase transition and belief propagation up to the condensation point. Finally, refined message passing techniques (such as survey propagation) may also beat this threshold.