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Soroosh ShafieezadehAbadeh (soroosh.shafieeepfl.ch) Abstract: This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains the unknown datagenerating distribution with high confidence. We then formulate a distributionally robust logistic regression model that minimizes a worstcase expected logloss function, where the worst case is taken over all distributions in the Wasserstein ball. We prove that this optimization problem admits a tractable reformulation and encapsulates the classical as well as the popular regularized logistic regression problems as special cases. We further propose a distributionally robust approach based on Wasserstein balls to compute upper and lower confidence bounds on the misclassification probability of the resulting classifier. These bounds are given by the optimal values of two highly tractable linear programs. We validate our theoretical outofsample guarantees through simulated and empirical experiments. Keywords: Distributionally robust optimization, logistic regression, Wasserstein distance Category 1: Robust Optimization Category 2: Stochastic Programming Citation: Risk Analytics and Optimization Chair, EPFL Download: [PDF] Entry Submitted: 09/30/2015 Modify/Update this entry  
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