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

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 leverage a connection between the sensor placement problem and sparse Gaussian processes~(SGP) to address this problem. Our approach uses SGPs and optimizes them using gradient descent in a sparsely supervised manner, which allows us to efficiently find solution placements in novel continuous environments. 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.

Kalvik Jakkala

My research interests include Bayesian learning and robotics.