Related papers: The Power of Subsampling in Submodular Maximizatio…
In this work, we present a combinatorial, deterministic single-pass streaming algorithm for the problem of maximizing a submodular function, not necessarily monotone, with respect to a cardinality constraint (SMCC). In the case the function…
We study the problem of finding a maximum matching in a graph given by an input stream listing its edges in some arbitrary order, where the quantity to be maximized is given by a monotone submodular function on subsets of edges. This…
Given a collection of monotone submodular functions, the goal of Two-Stage Submodular Maximization (2SSM) [Balkanski et al., 2016] is to restrict the ground set so an objective selected u.a.r. from the collection attains a high maximal…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…
We study the problem of maximizing a non-monotone submodular function subject to a cardinality constraint in the streaming model. Our main contribution is a single-pass (semi-)streaming algorithm that uses roughly $O(k / \varepsilon^2)$…
Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone. The case of non-monotone submodular maximization is less…
Data summarization has become a valuable tool in understanding even terabytes of data. Due to their compelling theoretical properties, submodular functions have been in the focus of summarization algorithms. These algorithms offer…
Submodular maximization has become established as the method of choice for the task of selecting representative and diverse summaries of data. However, if datapoints have sensitive attributes such as gender or age, such machine learning…
We consider the problem of maximizing a non-negative submodular function under the $b$-matching constraint, in the semi-streaming model. When the function is linear, monotone, and non-monotone, we obtain the approximation ratios of…
We study the problem of selecting a subset of vectors from a large set, to obtain the best signal representation over a family of functions. Although greedy methods have been widely used for tackling this problem and many of those have been…
Submodular optimization has numerous applications such as crowdsourcing and viral marketing. In this paper, we study the fundamental problem of non-negative submodular function maximization subject to a $k$-system constraint, which…
We briefly discuss the greedy method and a couple of its more efficient variants for approximately maximizing monotone submodular functions.
In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but…
In this paper, we propose a new framework for designing fast parallel algorithms for fundamental statistical subset selection tasks that include feature selection and experimental design. Such tasks are known to be weakly submodular and are…
In machine learning and big data, the optimization objectives based on set-cover, entropy, diversity, influence, feature selection, etc. are commonly modeled as submodular functions. Submodular (function) maximization is generally NP-hard,…
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…
Several large-scale machine learning tasks, such as data summarization, can be approached by maximizing functions that satisfy submodularity. These optimization problems often involve complex side constraints, imposed by the underlying…
We study parallel algorithms for the problem of maximizing a non-negative submodular function. Our main result is an algorithm that achieves a nearly-optimal $1/2 -\epsilon$ approximation using $O(\log(1/\epsilon) / \epsilon)$ parallel…
The sheer scale of modern datasets has resulted in a dire need for summarization techniques that identify representative elements in a dataset. Fortunately, the vast majority of data summarization tasks satisfy an intuitive diminishing…
For many optimization problems in machine learning, finding an optimal solution is computationally intractable and we seek algorithms that perform well in practice. Since computational intractability often results from pathological…