# Sensing Cox Processes via Posterior Sampling and Positive Bases

arXiv: https://arxiv.org/abs/2110.11181 · HTML: https://mlsanity.com/paper/2110.11181/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 56 references that are in the map.
- First posted on arXiv 21 Oct 2021.

## Builds on (most cited first, 20 of 20)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Simple Bayesian Algorithms for Best Arm Identification](https://mlsanity.com/paper/1602.08448/) (2016)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Mirrored Langevin Dynamics](https://mlsanity.com/paper/1802.10174/) (2018)
- [Wasserstein Control of Mirror Langevin Monte Carlo](https://mlsanity.com/paper/2002.04363/) (2020)
- [Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo](https://mlsanity.com/paper/1705.08964/) (2017)
- [The Why and How of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1401.5226/) (2014)
- [Gaussian process emulators for computer experiments with inequality constraints](https://mlsanity.com/paper/1606.01265/) (2016)
- [Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes](https://mlsanity.com/paper/1808.00831/) (2018)
- [Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm](https://mlsanity.com/paper/1312.6536/) (2013)
- [Poisson intensity estimation with reproducing kernels](https://mlsanity.com/paper/1610.08623/) (2016)
- [Finite-dimensional Gaussian approximation with linear inequality constraints](https://mlsanity.com/paper/1710.07453/) (2017)
- [Fast Bayesian Intensity Estimation for the Permanental Process](https://mlsanity.com/paper/1701.03535/) (2017)
- [Large-Scale Cox Process Inference using Variational Fourier Features](https://mlsanity.com/paper/1804.01016/) (2018)
- [Discovering Valuable Items from Massive Data](https://mlsanity.com/paper/1506.00935/) (2015)
- [Gaussian Process Modulated Cox Processes under Linear Inequality Constraints](https://mlsanity.com/paper/1902.10974/) (2019)
- [Adaptive Policies for Perimeter Surveillance Problems](https://mlsanity.com/paper/1810.02176/) (2018)

## Built on by (most cited first, 4 of 4)

- [Diversified Sampling for Batched Bayesian Optimization with Determinantal Point Processes](https://mlsanity.com/paper/2110.11665/) (2021)
- [Submodular Reinforcement Learning](https://mlsanity.com/paper/2307.13372/) (2023)
- [Active Exploration via Experiment Design in Markov Chains](https://mlsanity.com/paper/2206.14332/) (2022)
- [Near-Optimal Multi-Agent Learning for Safe Coverage Control](https://mlsanity.com/paper/2210.06380/) (2022)

## Abstract (arXiv)

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 (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.