LTF: A Label Transformation Framework for Correcting Label Shift

Distribution shift is a major obstacle to the deployment of current deep learning models on real-world problems. Let $Y$ be the class label and $X$ the features. We focus on one type of distribution shift, \textit{ label shift}, where the label marginal distribution $P_Y$ changes but the conditional distribution $P_{X|Y}$ does not. Most existing methods estimate the density ratio between the source- and target-domain label distributions by density matching. However, these methods are either computationally infeasible for large-scale data or restricted to shift correction for discrete labels. In this paper, we propose an end-to-end Label Transformation Framework (LTF) for correcting label shift, which implicitly models the shift of $P_Y$ and the conditional distribution $P_{X|Y}$ using neural networks. Thanks to the flexibility of deep networks, our framework can handle continuous, discrete, and even multi-dimensional labels in a unified way and is scalable to large data. Moreover, for high dimensional $X$, such as images, we find that the redundant information in $X$ severely degrades the estimation accuracy. To remedy this issue, we propose to match the distribution implied by our generative model and the target-domain distribution in a low-dimensional feature space that discards information irrelevant to $Y$. Both theoretical and empirical studies demonstrate the superiority of our method over previous approaches.