Label Shift Estimation for Class-Imbalance Problem: A Bayesian Approach

As a type of distribution shift, label shift occurs when the source and target domains have different label distributions $\mathbb{P}(Y)$ but identical conditional distributions of data given labels $\mathbb{P}(X|Y)$. Under a Bayesian framework, we propose a novel Maximum A Posteriori (MAP) model and a novel posterior sampling model for the label shift problem. We prove the MAP objective admits a unique optimum and derive an EM algorithm that converges to the global optimum. We propose a novel Adaptive Prior Learning (APL) model to adaptively select prior parameters given data. We use the Markov Chain Monte Carlo (MCMC) method in our posterior sampling model to estimate and correct for label shift. Our methods can effectively resolve class imbalance problems on large-scale datasets without fine-tuning the classifier. Experiments show that our model outperforms existing methods on a variety of label shift settings. Our code is available at https://github.com/ChangkunYe/MAPLS/.