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Motivated by data-driven decision making and sampling problems, we investigate probabilistic interpretations of Robust Optimization (RO). We establish a connection between RO and Distributionally Robust Stochastic Programming (DRSP), showing that the solution to any RO problem is also a solution to a DRSP problem. Specifically, we consider the case where multiple uncertain parameters belong to the...
We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the the number of observations is of the same magnitude as the number of variables of each observation, and the data set contains some (arbitrarily) corrupted observations. We propose a high-dimensional robust principal component analysis...
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