Sensing Cox Processes via Posterior Sampling and Positive Bases

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 emphminimal 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 (textscCox-Thompson) and top-two posterior sampling (textscTop2) 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.

Publication
Proceedings of the 25th International Conference on Artificial Intelligence and Statistics (AISTATS)