Related papers: Learning and Optimization with Submodular Function…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
We consider a class of sparsity-inducing regularization terms based on submodular functions. While previous work has focused on non-decreasing functions, we explore symmetric submodular functions and their \lova extensions. We show that the…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
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…
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 function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements…
We develop a framework for the distributed minimization of submodular functions. Submodular functions are a discrete analog of convex functions and are extensively used in large-scale combinatorial optimization problems. While there has…
Many sequential decision making problems can be formulated as an adaptive submodular maximization problem. However, most of existing studies in this field focus on pool-based setting, where one can pick items in any order, and there have…
Optimization problems often involve vector norms, which has led to extensive research on developing algorithms that can handle objectives beyond the $\ell_p$ norms. Our work introduces the concept of submodular norms, which are a versatile…
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…
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…
Submodularity is a key property in discrete optimization. Submodularity has been widely used for analyzing the greedy algorithm to give performance bounds and providing insight into the construction of valid inequalities for mixed-integer…
In Constraint Programming, constraints are usually represented as predicates allowing or forbidding combinations of values. However, some algorithms exploit a finer representation: error functions. Their usage comes with a price though: it…
Submodular functions are at the core of many machine learning and data mining tasks. The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions. In many data…
Statistical decision problems lie at the heart of statistical machine learning. The simplest problems are binary and multiclass classification and class probability estimation. Central to their definition is the choice of loss function,…
Many prediction domains, such as ad placement, recommendation, trajectory prediction, and document summarization, require predicting a set or list of options. Such lists are often evaluated using submodular reward functions that measure…
Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems.…
Training a Neural Network (NN) with lots of parameters or intricate architectures creates undesired phenomena that complicate the optimization process. To address this issue we propose a first modular approach to NN design, wherein the NN…
In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…