Abstract
The monitoring and forecasting of particulate matter (e.g., PM2.5) and gaseous pollutants (e.g., NO, NO2, and SO2) is of significant importance, as they have adverse impacts on human health. However, model performance can easily degrade due to data noises, environmental and other factors. This paper proposes a general solution to analyse how the noise level of measurements and hyperparameters of a Gaussian process model affect the prediction accuracy and uncertainty, with a comparative case study of atmospheric pollutant concentrations prediction in Sheffield, UK, and Peshawar, Pakistan. The Neumann series is exploited to approximate the matrix inverse involved in the Gaussian process approach. This enables us to derive a theoretical relationship between any independent variable (e.g., measurement noise level, hyperparameters of Gaussian process methods), and the uncertainty and accuracy prediction. In addition, it helps us to discover insights on how these independent variables affect the algorithm evidence lower bound. The theoretical results are verified by applying a Gaussian processes approach and its sparse variants to air quality data forecasting.
Highlights
It is generally believed that urban areas provide better opportunities in terms of economic, political, and social facilities compared to rural areas
To verify that the proposed solution can help to identify the impacts of σn2 and θ on the predition accuracy and uncertainty of Gaussian processes (GPs) model and its sparse variants such as the fully independent training conditional (FITC) [25] and variational free energy (VFE) [24] models, we conduct various experiments to process air quality data collected from Sheffield, UK, and Pershawar, Pakistan, during the time period of 24 June 2019–14 July for three weeks, which will be denoted as W1, W2, and W3 hereafter
This paper proposes a general method to investigate how the performance variation of a Gaussian process model can be attributed to hyperparameters and measurement noises, etc
Summary
It is generally believed that urban areas provide better opportunities in terms of economic, political, and social facilities compared to rural areas. More than fifty percent of people worldwide live in urban areas, and this percentage is increasing with time. This has led to several environmental issues in large cities, such as air pollution [1]. Many national and international organisations are actively working on understanding the behaviour of various air pollutants [7] This eventually leads to the development of air quality forecasting models so that people can be alerted in time [8]. The function values at the test inputs X∗ with dimensions of D × N can be denoted as f∗ , and we write the joint distribution of y and f∗ as y
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