We present a new approach to the design and implementation of probabilistic programming languages (PPLs), based on idea stochastically estimating probability density ratios necessary for inference. By relaxing usual PPL constraint that these densities be computed exactly, we are able eliminate many common restrictions in current PPLs, deliver language that, first time, simultaneously supports f...

We propose a framework for robust modeling of linear programming problems using uncertainty sets described by an arbitrary norm. We explicitly characterize the robust counterpart as a convex optimization problem that involves the dual norm of the given norm. Under a Euclidean norm we recover the second order cone formulation in BenTal and Nemirovski [1, 2], El Ghaoui et al. [8, 9], while under ...

this paper proposes a family of robust counterpart for uncertain linear programs (lp) which is obtained for a general definition of the uncertainty region. the relationship between uncertainty sets using norm bod-ies and their corresponding robust counterparts defined by dual norms is presented. those properties lead us to characterize primal and dual robust counterparts. the researchers show t...

This work introduces a robust formulation of the uncertain set covering problem combining the concepts of robust and probabilistic optimization and defines ’Γ-robust α-covers’. It is shown that the proposed robust uncertain set covering problem can be stated as a compact mixed-integer linear programming model which can be solved with modern computer software. This model is a natural extension o...

In this presentation, we study the applications of robust optimization in signal processing: robust beamforming in array and power control in wireless networks. First, the background of beamforming and the traditional diagonal loading (DL) method are introduced. Then, the robust beamforming designs are proposed by considering the worst-case distortionless and probabilistic constraints of the st...