We introduce a class of discrete point processes that we call the Submodular Point Processes (SPPs). These processes are characterized via a submodular (or supermodular) function, and naturally model notions of information, coverage and diversity, as well as cooperation. Unlike Log-submodular and Log-supermodular distributions (Log-SPPs) such as determinantal point processes (DPPs), SPPs are th...

Submodular and supermodular functions have found wide applicability in machine learning, capturing notions such as diversity and regularity, respectively. These notions have deep consequences for optimization, and the problem of (approximately) optimizing submodular functions has received much attention. However, beyond optimization, these notions allow specifying expressive probabilistic model...

This paper studies equilibrium selection in supermodular games based on perfect foresight dynamics. A normal form game is played repeatedly in a large society of rational agents. There are frictions: opportunities to revise actions follow independent Poisson processes. Each agent forms his belief about the future evolution of the action distribution in the society, and takes an action that maxi...

Several supermodular losses have been shown to improve the perceptual quality of image segmentation in a discriminative framework such as a structured output support vector machine (SVM). These loss functions do not necessarily have the same structure as the one used by the segmentation inference algorithm, and in general, we may have to resort to generic submodular minimization algorithms for ...

We provide a counterexample to the performance guarantee obtained in paper “Il’ev, V., Linker, N., 2006. Performance guarantees of greedy algorithm for minimizing supermodular set function on comatroid”, which was published Volume 171 European Journal Operational Research. point out where this error originates from proof main theorem.

We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture highorder interactions, which are intractable for existing approximate inference techniques such as belief propagation, mean field, and variants. We show that a recently proposed variational approach to inference in log-su...

This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent, statistically limit and lacunary sequences. Let θ be a lacunary sequence; the two nonnegative sequences x = (xk) and y = (yk) are said to be asymptotically ∆ m lacunary statistical(defined in [2]) equivalent of multiple L provided that for every > 0, lim r 1 hr { the numb...

number: 011-0137 Optimal stock allocation in single echelon inventory systems subject to a service constraint Annalisa Cesaro • Dario Pacciarelli • Dipartimento di Informatica e Automazione, Università Roma Tre, Via della Vasca Navale, 79, Rome I-00146, Italy [email protected] • [email protected] • phone:0039-06-57333394 POMS 20th Annual Conference Orlando, Florida U.S.A. May 1 t...

We introduce a class of discrete point processes that we call the Submodular Point Processes (SPPs). These processes are characterized via a submodular (or supermodular) function, and naturally model notions of information, coverage and diversity, as well as cooperation. Unlike Log-submodular and Log-supermodular distributions (Log-SPPs) such as determinantal point processes (DPPs), SPPs are th...