Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tightly bound modular loss functions, submodular functions or supermodular functions separately while maintaining polynomial time computation. In this work, a novel generic convex ...

In this paper we extend some recent results on the comparison of multivariate risk vectors w.r.t. supermodular and related orderings. We introduce a dependence notion called ‘weakly conditional increasing in sequence order’ that allows to conclude that ‘more dependent’ vectors in this ordering are also comparable w.r.t. the supermodular ordering. At the same time this ordering allows to compare...

We show that supermodular games satisfying sequential better-reply security possess a pure strategy perfect equilibrium and a strategically stable set of pure strategy equilibria. We illustrate that in continuous supermodular games, perfect equilibria may contain weakly dominated actions. Moreover, in discontinuous supermodular games satisfying sequential better-reply security, perfect equilibr...

In many economic applications involving comparisons of multivariate distributions, supermodularity of an objective function is a natural property for capturing a preference for greater interdependence. One multivariate distribution dominates another according to the supermodular stochastic ordering if it yields a higher expectation than the other for all supermodular objective functions. We pro...

We propose a closed architecture for data sampling in wireless sensor networks. Examples show that the proposed scheme outperforms the tradiotional layered scheme, both in terms of stable operating region as well as the end-to-end delays. We then propose a distributed routing scheme for a broad class of wireless sensor networks which converges (in the Cesaro sense) to the set of Cesaro-Wardrop ...

In many economic applications involving comparisons of multivariate distributions, supermodularity of an objective function is a natural property for capturing a preference for greater interdependence. One multivariate distribution dominates another according to the supermodular stochastic ordering if it yields a higher expectation than the other for all supermodular objective functions. We pro...

We establish an identity for $$Ef\left( \varvec{Y}\right) - Ef\left( \varvec{X}\right) $$ , when $$\varvec{X}$$ and $$\varvec{Y}$$ both have matrix variate skew-normal distributions the function f satisfies some weak conditions. The characteristic of skew normal distribution is then derived. make use it to derive necessary sufficient conditions comparison under six different orders, such as usu...

We take an order-centric approach to an incomplete-information version of the supermodular game (SG). In particular, we first introduce concepts related to ordered normal form games and the stochastic dominance order. Then, we work on a Bayesian SG, for which we show the existence of a monotone equilibrium and its monotonic trend as the player type distribution varies. Our results complement th...