Sensing Cox Processes via Posterior Sampling and Positive Bases
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Date
2022
Publication Type
Conference Paper
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yes
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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 the minimal description positive basis can be adapted to the covariance kernel, to 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 (Cox-TnomPsoN) and top-two posterior sampling (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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Publication status
published
Book title
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics
Journal / series
Volume
151
Pages / Article No.
6968 - 6989
Publisher
PMLR
Event
25th International Conference on Artificial Intelligence and Statistics (AISTATS 2022)
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Organisational unit
03908 - Krause, Andreas / Krause, Andreas
Notes
Funding
180544 - NCCR Catalysis (phase I) (SNF)