Cross-Domain Empirical Risk Minimization for Unbiased Long-Tailed Classification

We address the overlooked unbiasedness in existing long-tailed classification methods: we find that their overall improvement is mostly attributed to the biased preference of "tail" over "head", as the test distribution is assumed to be balanced; however, when the test is as imbalanced as the long-tailed training data---let the test respect Zipf's law of nature---the "tail" bias is no longer beneficial overall because it hurts the "head" majorities. In this paper, we propose Cross-Domain Empirical Risk Minimization (xERM) for training an unbiased test-agnostic model to achieve strong performances on both test distributions, which empirically demonstrates that xERM fundamentally improves the classification by learning better feature representation rather than the "head vs. tail" game. Based on causality, we further theoretically explain why xERM achieves unbiasedness: the bias caused by the domain selection is removed by adjusting the empirical risks on the imbalanced domain and the balanced but unseen domain.