  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. This
limitation restricts these approaches from scaling to large problems. We have
uncovered a novel connection between the sensor placement problem and sparse
Gaussian processes~(SGP). Our approach leverages SGPs and is gradient-based,
which allows us to efficiently find solution placements in 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.
