Machine learning models often suffer from performance degradation when dealing with class distributions that differ from the training distribution, a scenario commonly referred to as label shift. Addressing this challenge, this paper introduces Match, a novel adjustment approach that maximizes the likelihood of predicted probabilities under class prevalence constraints. Unlike existing methods such as retraining with instance re-weighting and the Bayes update rule, Match ensures that the adjusted class distribution aligns precisely with the prevalence estimates from quantifiers. By formulating the adjustment process as a binary integer linear optimization problem, Match benefits from efficient mixed-integer solvers. Extensive experiments demonstrate that Match outperforms the state-of-the-art in classifier adjustment with statistical significance, particularly in handling scenarios with imbalanced distributions.

An assumption often made in supervised learning is that the training and testing sets have the same label distribution. However, in real-life scenarios, this assumption rarely holds. For example, medical diagnosis result distributions change over time and across locations; fraud detection models must adapt as patterns of fraudulent activity shift; the category distribution of social media posts changes based on trending topics and user demographics. In the task of label shift estimation, the goal is to estimate the changing label distribution pt(y) in the testing set, assuming the likelihood p(x|y) does not change, implying no concept drift. In this paper, we propose a new approach for post-hoc label shift estimation, unlike previous methods that perform moment matching with confusion matrix estimated from a validation set or maximize the likelihood of the new data with an expectation-maximization algorithm. We aim to incrementally update the prior on each sample, adjusting each posterior for more accurate label shift estimation. The proposed method is based on intuitive assumptions on classifiers that are generally true for modern probabilistic classifiers. The proposed method relies on a weaker notion of calibration compared to other methods. As a post-hoc approach for label shift estimation, the proposed method is versatile and can be applied to any black-box probabilistic classifier. Experiments on CIFAR-10 and MNIST show that the proposed method consistently outperforms the current state-of-the-art maximum likelihood-based methods under different calibrations and varying intensities of label shift.