In this paper, we consider the problem of minimizing a non-smooth convex problem using first-order methods. The number of iterations required to guarantee a certain accuracy for ...
Support vector machines utilizing the 1-norm, typically set up as linear programs (Mangasarian, 2000; Bradley and Mangasarian, 1998), are formulated here as a completely unconstra...
Abstract. In this paper we unify divergence minimization and statistical inference by means of convex duality. In the process of doing so, we prove that the dual of approximate max...
We develop and analyze an algorithm for nonparametric estimation of divergence functionals and the density ratio of two probability distributions. Our method is based on a variati...
XuanLong Nguyen, Martin J. Wainwright, Michael I. ...
We develop and analyze M-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variatio...
XuanLong Nguyen, Martin J. Wainwright, Michael I. ...