Near-optimal Sensor Placements In Gaussian Processes

Abstract

When monitoring spatial phenomena, which are often modeled as Gaussian Processes (GPs), choosing sensor locations is a fundamental task. A common strategy is to place sensors at the points of highest entropy (variance) in the GP model. We propose a <i>mutual information</i> criteria, and show that it produces better placements. Furthermore, we prove that finding the configuration that maximizes mutual information is NP-complete. To address this issue, we describe a polynomial-time approximation that is within (1 -- 1/<i>e</i>) of the optimum by exploiting the <i>submodularity</i> of our criterion. This algorithm is extended to handle local structure in the GP, yielding significant speedups. We demonstrate the advantages of our approach on two real-world data sets.