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The problem of quickest detection of a change in the distribution of streaming data is considered. It is assumed that the pre-change distribution is known, while the only information about the post-change is through a (small) set of labeled data. This post-change data is used in a data-driven minimax robust framework, where an uncertainty set for the post-change distribution is constructed. The robust change detection problem is studied in an asymptotic setting where the mean time to false alarm goes to infinity. It is shown that the least favorable distribution (LFD) is an exponentially tilted version of the pre-change density and can be obtained efficiently. A Cumulative Sum (CuSum) test based on the LFD, which is referred to as the distributionally robust (DR) CuSum test, is then shown to be asymptotically robust. The results are extended to the case with multiple post-change uncertainty sets and validated using synthetic and real data examples. 

We study the problem of out-of-distribution (OOD) detection, that is, detecting whether a machine learning (ML) model's output can be trusted at inference time. While a number of tests for OOD detection have been proposed in prior work, a formal framework for studying this problem is lacking. We propose a definition for the notion of OOD that includes both the input distribution and the ML model, which provides insights for the construction of powerful tests for OOD detection. We also propose a multiple hypothesis testing inspired procedure to systematically combine any number of different statistics from the ML model using conformal p-values. We further provide strong guarantees on the probability of incorrectly classifying an in-distribution sample as OOD. In our experiments, we find that threshold-based tests proposed in prior work perform well in specific settings, but not uniformly well across different OOD instances. In contrast, our proposed method that combines multiple statistics performs uniformly well across different datasets and neural networks architectures.