相关论文: Multivariate Submodular Optimization

Recent years have seen many algorithmic advances in the area of submodular optimization: (SO) $\min/\max~f(S): S \in \mathcal{F}$, where $\mathcal{F}$ is a given family of feasible sets over a ground set $V$ and $f:2^V \rightarrow…

Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…

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…

As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical…

Submodular optimization is a fundamental problem with many applications in machine learning, often involving decision-making over datasets with sensitive attributes such as gender or age. In such settings, it is often desirable to produce a…

We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…

Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…

We consider the following class of submodular k-multiway partitioning problems: (Sub-$k$-MP) $\min \sum_{i=1}^k f(S_i): S_1 \uplus S_2 \uplus \cdots \uplus S_k = V \mbox{ and } S_i \neq \emptyset \mbox{ for all }i\in [k]$. Here $f$ is a…

Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…

Subset selection tasks, arise in recommendation systems and search engines and ask to select a subset of items that maximize the value for the user. The values of subsets often display diminishing returns, and hence, submodular functions…

Submodular function minimization (SFM) is a fundamental discrete optimization problem which generalizes many well known problems, has applications in various fields, and can be solved in polynomial time. Owing to applications in computer…

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…

Submodular optimization finds applications in machine learning and data mining. In this paper, we study the problem of maximizing functions of the form $h = f-c$, where $f$ is a monotone, non-negative, weakly submodular set function and $c$…

Continuous submodular functions are a category of generally non-convex/non-concave functions with a wide spectrum of applications. The celebrated property of this class of functions - continuous submodularity - enables both exact…

Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but…

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…

Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an…

Submodularity is a discrete domain functional property that can be interpreted as mimicking the role of the well-known convexity/concavity properties in the continuous domain. Submodular functions exhibit strong structure that lead to…

Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the…

We investigate a more generalized form of submodular maximization, referred to as $k$-submodular maximization, with applications across social networks and machine learning domains. In this work, we propose the multilinear extension of…