Bayesian Optimisation for Active Monitoring of Air Pollution

TL;DR

The paper addresses efficient placement of ground-level air-pollution sensors by applying Bayesian optimisation with a hierarchical Bayesian GP prior across cities. It couples Monte Carlo inference with importance weighting to adapt hyperparameters at test time, and evaluates on satellite NO2 data and London data using Expected Improvement as the acquisition. The results show improved sensor-placement metrics over baselines in urban settings and illustrate interpretable hyperparameters that reveal local and regional pollution structure, highlighting the method's practical potential for low-cost, scalable monitoring. The work also discusses limitations related to temporal dynamics and sensor uncertainty, and outlines future extensions to temporal modelling and kernel design to enhance real-world deployment.

Abstract

Air pollution is one of the leading causes of mortality globally, resulting in millions of deaths each year. Efficient monitoring is important to measure exposure and enforce legal limits. New low-cost sensors can be deployed in greater numbers and in more varied locations, motivating the problem of efficient automated placement. Previous work suggests Bayesian optimisation is an appropriate method, but only considered a satellite data set, with data aggregated over all altitudes. It is ground-level pollution, that humans breathe, which matters most. We improve on those results using hierarchical models and evaluate our models on urban pollution data in London to show that Bayesian optimisation can be successfully applied to the problem.

Figures (10)

• Figure 1: Visualisation of the hierarchical structure adopted. The bottom level is the observed data $\mathcal{D}$. It is modelled using GPs, which are defined by their hyperparameters $\theta$. The distribution of the GP hyperparameters is captured by $\eta$. The hyperparameters $\theta$ are independent given $\eta$.
• Figure 2: Examples of data snapshots from the satellite data set. Selection examples 1, 2 and 3 are the strongest, median and weakest images from the selection subset, respectively. The strong example is adapted from hellan_optimising_2020_arxiv. Crosses indicate missing data.
• Figure 3: Examples of data from the LAQN data set. The distances are from the most south-westerly monitoring station, in Beech outside Alton in Hampshire. Note that not all sensors are available each day, that the location of the maximum varies and the strong clustering in central London.
• Figure 4: Results on strong subset of satellite data. Our values in navy (darkest) compared to values in hellan_optimising_2020_arxiv in orange (lightest) marked with $\dagger$. The baseline 'Random' is shown in grey (medium, different pattern). The results obtained are better than those in existing work, and both out-compete the random baseline. $\hat{x}$ is the estimated maximiser and $x^*$ the true maximiser. $\hat{y}$ and $y^*$ are the true concentration values at $\hat{x}$ and $x^*$, respectively.
• Figure 5: Results on selection subset of satellite data. The legend and variable definitions are given in \ref{['fig:satellite-strong-res']}. Values in orange marked with $\dagger$ are from hellan_optimising_2020_arxiv. The new results are an improvement on those in existing work when considering the ratio metric; the three new results mostly lie on top of each other, and the three old results and the baseline mostly lie on top of each other. The baseline is competitive on the distance metric.