Related papers: Sensor placement minimizing the state estimation m…
The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a $1-1/e$ factor. Although it is well known that this guarantee is essentially…
We consider the problem of maximizing non-negative non-decreasing set functions. Although most of the recent work focus on exploiting submodularity, it turns out that several objectives we encounter in practice are not submodular.…
Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…
Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality…
We present new tight performance guarantees for the greedy maximization of nondecreasing submodular set functions. Our main result first provides a performance guarantee in terms of the overlap of the optimal and greedy solutions. As a…
A classic problem is the estimation of a set of parameters from measurements collected by only a few sensors. The number of sensors is often limited by physical or economical constraints and their placement is of fundamental importance to…
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…
Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…
The standard greedy algorithm has been recently shown to enjoy approximation guarantees for constrained non-submodular nondecreasing set function maximization. While these recent results allow to better characterize the empirical success of…
This paper presents two new greedy sensor placement algorithms, named minimum nonzero eigenvalue pursuit (MNEP) and maximal projection on minimum eigenspace (MPME), for linear inverse problems, with greater emphasis on the MPME algorithm…
Submodular functions -- functions exhibiting diminishing returns -- are central to machine learning. When the objective is monotone and non-negative, the greedy algorithm achieves a tight $63\%$ approximation. But many practical objectives…
This paper considers a set of sensors, which as a group are tasked with taking measurements of the environment and sending a small subset of the measurements to a centralized data fusion center, where the measurements will be used to…
In this paper, the sparse sensor placement problem for least-squares estimation is considered, and the previous novel approach of the sparse sensor selection algorithm is extended. The maximization of the determinant of the matrix which…
Weak submodularity is a natural relaxation of the diminishing return property, which is equivalent to submodularity. Weak submodularity has been used to show that many (monotone) functions that arise in practice can be efficiently maximized…
The problem of optimally placing sensors under a cost constraint arises naturally in the design of industrial and commercial products, as well as in scientific experiments. We consider a relaxation of the full optimization formulation of…
In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…
In this study, a nondominated-solution-based multi-objective greedy method is proposed and applied to a sensor selection problem based on the multiple indices of the optimal design of experiments. The proposed method simultaneously…
In this paper, we study stochastic submodular maximization problems with general matroid constraints, that naturally arise in online learning, team formation, facility location, influence maximization, active learning and sensing objective…
With the rising importance of large-scale network control, the problem of actuator placement has received increasing attention. Our goal in this paper is to find a set of actuators minimizing the metric that measures the average energy…
We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy…