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arXiv · 2110.11181

Sensing Cox Processes via Posterior Sampling and Positive Bases

Mojmír Mutný·Andreas Krause
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Abstract

We study adaptive sensing of Cox point processes, a widely used model from spatial statistics. We introduce three tasks: maximization of captured events, search for the maximum of the intensity function and learning level sets of the intensity function. We model the intensity function as a sample from a truncated Gaussian process, represented in a specially constructed positive basis. In this basis, the positivity constraint on the intensity function has a simple form. We show how an minimal description positive basis can be adapted to the covariance kernel, non-stationarity and make connections to common positive bases from prior works. Our adaptive sensing algorithms use Langevin dynamics and are based on posterior sampling (\textsc{Cox-Thompson}) and top-two posterior sampling (\textsc{Top2}) principles. With latter, the difference between samples serves as a surrogate to the uncertainty. We demonstrate the approach using examples from environmental monitoring and crime rate modeling, and compare it to the classical Bayesian experimental design approach.

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Mojmír Mutný, Andreas Krause. 2021-10-21. Sensing Cox Processes via Posterior Sampling and Positive Bases. https://arxiv.org/abs/2110.11181

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