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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. 

Discontinuities can be fairly arbitrary but also cause a significant impact on outcomes in social systems. Indeed, their arbitrariness is why they have been used to infer causal relationships among variables in numerous settings. Regression discontinuity from econometrics assumes the existence of a discontinuous variable that splits the population into distinct partitions to estimate causal effects. Here we consider the design of partitions for a given discontinuous variable to optimize a certain effect. To do so, we propose a quantization-theoretic approach to optimize the effect of interest, first learning the causal effect size of a given discontinuous variable and then applying dynamic programming for optimal quantization design of discontinuities that balance the gain and loss in the effect size. We also develop a computationally-efficient reinforcement learning algorithm for the dynamic programming formulation of optimal quantization. We demonstrate our approach by designing optimal time zone borders for counterfactuals of social capital.