An Improved Greedy Algorithm for Subset Selection in Linear Estimation

TL;DR

This paper introduces an enhanced greedy algorithm for selecting optimal observation locations in spatial fields, improving computational efficiency and solution quality for linear estimation tasks.

Contribution

The paper proposes a novel approach that reduces computational complexity by restricting the search space to prediction locations and clique centroids, enhancing greedy algorithm performance.

Findings

Improved solution quality in simulations

Reduced computational runtime

Effective in selecting observation locations

Abstract

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 can be taken at any location in the continuous field, and the covariance between the field values at different points is given by the widely used squared exponential covariance function. One approach for observation selection is to perform a grid discretization of the space and obtain an approximate solution using the greedy algorithm. The solution quality improves with a finer grid resolution but at the cost of increased computation. We propose a method to reduce the computational complexity, or conversely to increase solution quality, of the greedy algorithm by considering a search space consisting only of prediction locations and centroids of cliques formed by the prediction locations. We demonstrate the effectiveness of our proposed approach in simulation, both in terms of solution quality and runtime.