Characterizing Out-of-Distribution Error via Optimal Transport

Out-of-distribution (OOD) data poses serious challenges in deployed machine learning models, so methods of predicting a model's performance on OOD data without labels are important for machine learning safety. While a number of methods have been proposed by prior work, they often underestimate the actual error, sometimes by a large margin, which greatly impacts their applicability to real tasks. In this work, we identify pseudo-label shift, or the difference between the predicted and true OOD label distributions, as a key indicator to this under-estimation. Based on this observation, we introduce a novel method for estimating model performance by leveraging optimal transport theory, Confidence Optimal Transport (COT), and show that it provably provides more robust error estimates in the presence of pseudo label shift. Additionally, we introduce an empirically-motivated variant of COT, Confidence Optimal Transport with Thresholding (COTT), which applies thresholding to the individual transport costs and further improves the accuracy of COT's error estimates. We evaluate COT and COTT on a variety of standard benchmarks that induce various types of distribution shift -synthetic, novel subpopulation, and natural -and show that our approaches significantly outperform existing state-of-the-art methods with up to 3x lower prediction errors. Our code can be found at https://github.com/luyuzhe111/COT . Performance prediction on unlabeled data has previously been shown to be impossible without imposing additional constraints over the unknown target distribution [7, 11, 5, 26] , due to the fact that target samples may take any label. Thus, the feasibility of this task is dependent on what assumptions we make regarding the shift between the train and target distributions. Prior works often make the assumption that the conditional density P (y|x) remains fixed in the presence of covariate shift [37] .