Supermodularity has long been regarded as a natural notion of complementarities in individual decision making; it was introduced as such in the nineteenth century by Edgeworth and Pareto. But supermodularity is not an ordinal property. We study the ordinal content of assuming a supermodular utility, i.e. what it means for the individual’s underlying preferences. We show that supermodularity is ...

This paper defines weak-α-supermodularity for set functions. It shows that minimizing such functions under cardinality constrains is a common task in machine learning and data mining. Moreover, any problem whose objective function exhibits this property benefits from a greedy extension phase. Explicitly, let S∗ be the optimal set of cardinality k that minimizes f and let S0 be an initial soluti...

We introduce a constrained optimal transport problem where origins x can only be transported to destinations y≥x. Our statistical motivation is describe the sharp upper bound for variance of treatment effect Y−X given marginals when monotone, or Y≥X. thus focus on supermodular costs (or submodular rewards) and coupling P∗ that all such yields bound. This admits manifold characterizations—geomet...

Community partition is an important problem in many areas, such as biology networks and social networks. The objective of this to analyze the relationships among data via network topology. In article, we consider community under independent cascade (IC) model We formulate a combinatorial optimization that aims at partitioning given into disjoint <inline-formula xmlns:mml="http://www.w3.org/1998...

This paper compares n-dimensional random vectors in terms of their interdependence. We adopt the stochastic dominance approach, relating orderings of interdependence expressed directly in terms of joint probability distributions to orderings expressed indirectly through properties of objective functions whose expectations are used to evaluate distributions. Since the expected values of additive...

Slack and margin rescaling are variants of the structured output SVM. They define convex surrogates to task specific loss functions, which, when specialized to nonadditive loss functions for multi-label problems, yield extensions to increasing set functions. We demonstrate in this paper that we may use these concepts to define polynomial time convex extensions of arbitrary supermodular function...

Abstract This paper establishes relationships between static Nash equilibria and dynamic Markov perfect equilibria of tariff and quota retaliation games. In supermodular games where tariffs are strategic complements, the steady state of every, symmetric Markov perfect equilibrium must have lower tariffs than in the static equilibrium. If tariffs are strategic substitutes, tariffs in the dynamic...

We de®ne the base polytope B…P ; g† of a partially ordered set P and a supermodular function g on the ideals of P as the convex hull of the incidence vectors of all linear extensions of P . This new class of polytopes contains, among others, the base polytopes of supermodular systems and permutahedra as special cases. After introducing the notion of compatibility for g, we give a complete linea...

I study price competition in settings where end products are combinations of components supplied by different monopolists, nesting standard models of perfect complements and imperfect substitutes. I show sufficient conditions for a discrete-choice demand system to yield demand for each product which is logconcave in price, and has log-increasing differences in own and another product’s price, l...

Given a linear system, we consider the expected energy to move from the origin to a uniformly random point on the unit sphere as a function of the set of actuated variables. We show this function is not necessarily supermodular, correcting some claims in the existing literature.