Open Set Label Shift with Test Time Out-of-Distribution Reference

Open set label shift (OSLS) occurs when label distributions change from a source to a target distribution, and the target distribution has an additional out-of-distribution (OOD) class.In this work, we build estimators for both source and target open set label distributions using a source domain in-distribution (ID) classifier and an ID/OOD classifier. With reasonable assumptions on the ID/OOD classifier, the estimators are assembled into a sequence of three stages: 1) an estimate of the source label distribution of the OOD class, 2) an EM algorithm for Maximum Likelihood estimates (MLE) of the target label distribution, and 3) an estimate of the target label distribution of OOD class under relaxed assumptions on the OOD classifier.The sampling errors of estimates in 1) and 3) are quantified with a concentration inequality.The estimation result allows us to correct the ID classifier trained on the source distribution to the target distribution without retraining.Experiments on a variety of open set label shift settings demonstrate the effectiveness of our model in both estimation error and classification accuracy.