Distributionally Robust Binary Probit Regression Model

Binary probit regression is a typical model for classification problems. This paper proposes a novel distributionally robust method to estimate the parameters in binary probit regression model. We adopt the Wasserstein metric to establish the ambugity set of real distributions centered at the uniform distribution. If the size of ambugity and some hyperparameter are chosen judiciously, our distributionally robust binary probit regression model may perform well. We also discuss the tractable reformulation of the distributionally robust binary probit model and its out-of-sample performance guarantees. All results are shown in numerical experiments on UCI adult data.