Related papers: Maximizing submodular functions using probabilisti…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…
Certifying feasibility in decision-making, critical in many industries, can be framed as a constraint satisfaction problem. This paper focuses on characterising a subset of parameter values from an a priori set that satisfy constraints on a…
Submodular width is a central structural measure governing the complexity of conjunctive query evaluation. In this paper we recast submodular width in geometric terms. We how that submodular width can be approximated, up to a factor $3/2$,…
We explore some connections between association schemes and the analyses of the semidefinite programming (SDP) based convex relaxations of combinatorial optimization problems in the Lov\'{a}sz--Schrijver lift-and-project hierarchy. Our…
We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a nondecreasing submodular…
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this…
Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum…
Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow…
Dense subgraph extraction is a fundamental problem in graph analysis and data mining, aimed at identifying cohesive and densely connected substructures within a given graph. It plays a crucial role in various domains, including social…
DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others.…
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…
The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and…
Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint…
The main result of the paper is motivated by the following two, apparently unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising $k$ disjoint branchings $B_i$…
Many combinatorial problems arising in machine learning can be reduced to the problem of minimizing a submodular function. Submodular functions are a natural discrete analog of convex functions, and can be minimized in strongly polynomial…
The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a $1-1/e$ factor. Although it is well known that this guarantee is essentially…