Label Shift Estimation With Incremental Prior Update
This work addresses label shift estimation for applications like medical diagnosis and fraud detection, offering a versatile post-hoc solution, though it is incremental as it builds on existing methods with weaker calibration assumptions.
The paper tackles the problem of label shift estimation in supervised learning, where the label distribution changes between training and testing sets, by proposing a post-hoc method that incrementally updates priors on each sample. The method outperforms state-of-the-art maximum likelihood-based approaches on CIFAR-10 and MNIST datasets under various calibration and shift intensities.
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 $p_t(y)$ 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.