Related papers: Composable Coresets for Constrained Determinant Ma…
Determinantal point processes (DPPs) are well known models for diverse subset selection problems, including recommendation tasks, document summarization and image search. In this paper, we discuss a greedy deterministic adaptation of k-DPP.…
For the problem of maximizing a monotone, submodular function with respect to a cardinality constraint $k$ on a ground set of size $n$, we provide an algorithm that achieves the state-of-the-art in both its empirical performance and its…
In recent years, the capacitated center problems have attracted a lot of research interest. Given a set of vertices $V$, we want to find a subset of vertices $S$, called centers, such that the maximum cluster radius is minimized. Moreover,…
A saturated D-optimal design is a {+1,-1} square matrix of given order with maximal determinant. We search for saturated D-optimal designs of orders 19 and 37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are optimal.…
In this work, we study the problem of monotone non-submodular maximization with partition matroid constraint. Although a generalization of this problem has been studied in literature, our work focuses on leveraging properties of partition…
We present an efficient coresets-based neural network compression algorithm that sparsifies the parameters of a trained fully-connected neural network in a manner that provably approximates the network's output. Our approach is based on an…
Finding point configurations, that yield the maximum polarization (Chebyshev constant) is gaining interest in the field of geometric optimization. In the present article, we study the problem of unconstrained maximum polarization on compact…
We study the $k$-means problem for a set $\mathcal{S} \subseteq \mathbb{R}^d$ of $n$ segments, aiming to find $k$ centers $X \subseteq \mathbb{R}^d$ that minimize $D(\mathcal{S},X) := \sum_{S \in \mathcal{S}} \min_{x \in X} D(S,x)$, where…
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…
Regret minimizing sets are a very recent approach to representing a dataset D with a small subset S of representative tuples. The set S is chosen such that executing any top-1 query on S rather than D is minimally perceptible to any user.…
In the kernel clustering problem we are given a (large) $n\times n$ symmetric positive semidefinite matrix $A=(a_{ij})$ with $\sum_{i=1}^n\sum_{j=1}^n a_{ij}=0$ and a (small) $k\times k$ symmetric positive semidefinite matrix $B=(b_{ij})$.…
We consider the Top-$K$ selection problem, which aims to identify the largest $K$ elements in an array. Top-$K$ selection arises in many machine learning algorithms and often becomes a bottleneck on accelerators, which are optimized for…
Diversity is an important principle in data selection and summarization, facility location, and recommendation systems. Our work focuses on maximizing diversity in data selection, while offering fairness guarantees. In particular, we offer…
Coresets are among the most popular paradigms for summarizing data. In particular, there exist many high performance coresets for clustering problems such as $k$-means in both theory and practice. Curiously, there exists no work on…
Accurate coresets are a weighted subset of the original dataset, ensuring a model trained on the accurate coreset maintains the same level of accuracy as a model trained on the full dataset. Primarily, these coresets have been studied for a…
Imagine we want to split a group of agents into teams in the most \emph{efficient} way, considering that each agent has their own preferences about their teammates. This scenario is modeled by the extensively studied \textsc{Coalition…
Let $\mathrm{R}$ be a real closed field, and $\mathrm{D} \subset \mathrm{R}$ an ordered domain. We describe an algorithm that given as input a polynomial $P \in \mathrm{D} [ X_{1},\ldots,X_{k} ]$, and a finite set, $\mathcal{A}= \{ p_{1},…
Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized…
This article provides numerical evidence that under volume constraint the ball is the set which maximizes the perimeter of the least-perimeter partition into cells with prescribed areas. We introduce a numerical maximization algorithm which…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…