Related papers: Composable Core-sets for Determinant Maximization:…
Given a set of $n$ vectors in $\mathbb{R}^d$, the goal of the \emph{determinant maximization} problem is to pick $k$ vectors with the maximum volume. Determinant maximization is the MAP-inference task for determinantal point processes (DPP)…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Core-sets refer to subsets of data that maximize some function that is commonly a diversity or group requirement. These subsets are used in place of the original data to accomplish a given task with comparable or even enhanced performance…
We study algorithms for construction of composable coresets for the task of Determinant Maximization under partition constraint. Given a point set $V\subset \mathbb{R}^d$ that is partitioned into $s$ groups $V_1,\cdots, V_s$, and integers…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…
It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…
Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find…
A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two…
We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors $V\subseteq \Re^d$, we say a set $U\subseteq V$ is an $\alpha$-spectral spanner if for all $v\in V$ there is a…
We present SimultaneousGreedys, a deterministic algorithm for constrained submodular maximization. At a high level, the algorithm maintains $\ell$ solutions and greedily updates them in a simultaneous fashion. SimultaneousGreedys achieves…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
In this work we consider the diversity maximization problem, where given a data set $X$ of $n$ elements, and a parameter $k$, the goal is to pick a subset of $X$ of size $k$ maximizing a certain diversity measure. [CH01] defined a variety…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy…
A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances…
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this…
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…
The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…
We introduce the problem of maximizing approximately $k$-submodular functions subject to size constraints. In this problem, one seeks to select $k$-disjoint subsets of a ground set with bounded total size or individual sizes, and maximum…