Efficient Sensor Placement from Regression with Sparse Gaussian Processes in Continuous and Discrete Spaces

TL;DR

This paper introduces a scalable, gradient-based method for sensor placement using sparse Gaussian processes, effective in both continuous and discrete environments, and outperforming existing approaches in speed and quality.

Contribution

The paper presents a novel variational approximation approach for sensor placement that enables efficient gradient-based optimization in continuous spaces, extending to discrete environments.

Findings

Achieves comparable or better mutual information scores than state-of-the-art methods.

Significantly reduces computation time for large-scale sensor placement.

Enables fast sensor placement suitable for robotic path planning.

Abstract

The sensor placement problem is a common problem that arises when monitoring correlated phenomena, such as temperature, precipitation, and salinity. Existing approaches to this problem typically formulate it as the maximization of information metrics, such as mutual information~(MI), and use optimization methods such as greedy algorithms in discrete domains, and derivative-free optimization methods such as genetic algorithms in continuous domains. However, computing MI for sensor placement requires discretizing the environment, and its computation cost depends on the size of the discretized environment. These limitations restrict these approaches from scaling to large problems. We present a novel formulation to the SP problem based on variational approximation that can be optimized using gradient descent, allowing us to efficiently find solutions in continuous domains. We generalize our method to also handle discrete environments. Our experimental results on four real-world datasets demonstrate that our approach generates sensor placements consistently on par with or better than the prior state-of-the-art approaches in terms of both MI and reconstruction quality, all while being significantly faster. Our computationally efficient approach enables both large-scale sensor placement and fast robotic sensor placement for informative path planning algorithms.