Mutual Information Input Selector and Probabilistic Machine Learning Utilisation for Air Pollution Proxies  
[PERSON]  
1 Institute for Atmospheric and Earth System Research/Physics, Helsinki University, FI-00560 Helsinki, Finland; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,  
Air quality indicators are typically monitored by environmental or government authorities using networks of fixed monitoring stations [6], equipped with instruments specialised for measuring a number of pollutants, such as carbon monoxide (CO), nitrogen oxides (NOx), sulphur dioxide (SO\({}_{2}\)), ozone (O\({}_{3}\)) and particulate matter (PM) [7]. In practice, a comprehensive measurement covering a large area may not always be possible as air pollutant analysers are generally complicated, bulky and labour-intensive [7; 8]. Furthermore, instrument failure, fault in data acquisition or data corruption often result in missing data during research campaigns or continuous measurements [9; 10; 11]. If the data gap is relatively large, interpolation methods become ineffective. As a result, these problems pose a significant obstacle for comprehensive air pollution data analysis and time series prediction scheme. There are several solutions in order to deal with the aforementioned challenges, including low-cost air quality sensor networks [12], chemical transport simulation models [13] and satellite remote sensing data [14]. Here, we propose the solution by developing a pollutant proxy that is also known as a model or an estimator. A pollutant proxy can be defined as a mathematical model that estimates an unobserved air pollutant using other measured variables. Such a proxy acts as a virtual sensor or an expert system to fill missing data or to substitute one or more real measurements, thus the number of operated instruments can be minimised leading to a reduction in operational cost as well as the operators involved. Therefore, the area with pollution information can also be widened. A pollutant proxy is also useful to support scientists in studying the impact of relevant variables to pollutants. Their relationship can be simulated and then analysed. Physics-based approaches are usually first to solve the aforementioned problems. These are models based on the fundamental description of atmospheric physical and chemical processes, such as Lagrangian and Eulerian models [15]. However, this approach is very computationally demanding. Simple statistical predictive models are usually the next attempt to solve the aforementioned problems, such as described in [PERSON] et al. [16], [PERSON] et al. [17], [PERSON] et al. [18], [PERSON] et al. [19], [PERSON] et al. [20]. However, these proxies may not always be suitable or perform well due to the poor input choice, nonlinearity in data and the complexity in establishing appropriate physics-based models. As an alternative approach, data-driven methods have recently gained much attention for developing pollutant proxies. For examples, various types of data-driven O\({}_{3}\) proxies were developed based on adaptive neuro-fuzzy inference by [PERSON] [21], artificial neural network (ANN) by [PERSON] et al. [22], [PERSON] et al. [23], support vector machine (SVM) by [PERSON] et al. [24] and based on ANN and SVM by [PERSON] et al. [25]. However, those methods mainly attempt to use all input combinations to obtain the best model performance during the training phase. This method may not always be effective for large data sets because of the computational cost and analysis issues. Recently, a large number of instruments involved in research campaigns as well as continuous measurements produces massive amounts of data. Additionally, many developed methods are mostly based on deterministic data-driven approaches where these proxies only estimate mean values of pollutant concentrations. Consequently, these proxies are unable to evaluate and assess the estimation uncertainty.