Machine learning (ML) algorithms can often differ in performance across domains.

The supplemental material is organized as follows. Section A provides the results of all the additional synthetic experiments and real data results for various kernel-based methods and the detailed settings. Section B describes the algorithm details we use in Section A. In Section C, we provide some useful lemmas and all the technical proofs of the theoretical results in the main text. In this section, we provide more experiment results, including KRR (Section A.1), KQR for various Section A.7. A.1 Kernel ridge regression For the squared loss, we consider the following two examples. TIRW estimator still performs significantly better. A.2 Kernel quantile regression For the check loss, we consider the following two examples.

Such a phenomenon is illustrated in Figure 1 where the learned predictive function from the source data may significantly differ from the true function.

However, sampling is not the only source of uncertainty. In practice, distributions change between locations and across time.

However, some marginal OOD samples actually have close semantic contents to the in-distribution (ID) sample, which makes determining the OOD sample a Sorites Paradox.