Discrepancy norm: approximation and variations

Abstract This paper introduces an approach for the minimization of the discrepancy norm. The general idea is to replace the infinity norms appearing in the definition by L p norms which are differentiable and to make use of this approximation for local optimization. We will show that the discrepancy norm can be approximated up to any ε and the robustness of this approximation is shown. Moreover, analytical formulation of the derivative of the discrepancy correlation function is given. In a following step we extend the results to higher dimensional data and derive the related forms for approximations and differentiations