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Submodular functions and variants, through their ability to characterize diversity and coverage, have emerged as a key tool for data selection and summarization. Many recent approaches to learn submodular functions suffer from limited…
We address the problem of maximizing an unknown submodular function that can only be accessed via noisy evaluations. Our work is motivated by the task of summarizing content, e.g., image collections, by leveraging users' feedback in form of…
We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified.…
Balog and Wooley have recently proved that any subset $A$ of either real numbers or of a prime finite field can be decomposed into two parts $U$ and $V$, one of small additive energy and the other of small multiplicative energy. In the case…
In the context of online interactive machine learning with combinatorial objectives, we extend purely submodular prior work to more general non-submodular objectives. This includes: (1) those that are additively decomposable into a sum of…
We consider minimization problems with bisubmodular objective functions. We propose valid inequalities, namely the poly-bimatroid inequalities, and provide a complete linear description of the convex hull of the epigraph of a bisubmodular…
Submodularity is desirable for a variety of objectives in content selection where the current neural encoder-decoder framework is inadequate. However, it has so far not been explored in the neural encoder-decoder system for text generation.…
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. It is desirable to classify the computational complexity of VCSPs depending on a fixed set of allowed cost functions in the input.…
An important tool in the study of the complexity of Constraint Satisfaction Problems (CSPs) is the notion of a relational clone, which is the set of all relations expressible using primitive positive formulas over a particular set of base…
When approaching to problems in computer science, we often encounter situations where a subset of a finite set maximizing some utility function needs to be selected. Some of such utility functions are known to be approximately submodular.…
We study a natural measurable selection problem for which the standard uniformisation theorems do not seem to apply directly, yet a Borel selector exists. More precisely, we consider families of finite dimensional functions that admit…
This work explores the novel idea of learning a submodular scoring function to improve the specificity/selectivity of existing feature attribution methods. Submodular scores are natural for attribution as they are known to accurately model…
Idempotent Boolean functions form a highly structured subclass of Boolean functions that is closely related to rotation symmetry under a normal-basis representation and to invariance under a fixed linear map in a polynomial basis. These…
We demonstrate the usefulness of submodularity in statistics as a characterization of the difficulty of the \emph{search} problem of feature selection. The search problem is the ability of a procedure to identify an informative set of…
This article provides a comprehensive exploration of submodular maximization problems, focusing on those subject to uniform and partition matroids. Crucial for a wide array of applications in fields ranging from computer science to systems…
The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…
We consider the problem of linearizing a pseudo-Boolean function $f : \{0,1\}^n \to \mathbb{R}$ by means of $k$ Boolean functions. Such a linearization yields an integer linear programming formulation with only $k$ auxiliary variables. This…
Maximizing a submodular function has a wide range of applications in machine learning and data mining. One such application is data summarization whose goal is to select a small set of representative and diverse data items from a large…
Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…
Compounding submodular monotone (i.e. 2-alternating) set functions on a finite set preserves this property, as shown in 2010. A natural generalization to k-alternating functions was presented in 2018, however hardly readable because of page…