## 4 PM\({}_{2.5}\) Estimation
### Machine Learning (ML) for PM2.5 Estimation  
Nowadays, several studies have used machine learning (ML) techniques, including RF model, aiming to increase the accuracy in prediction of PM concentrations, since these models are flexible in nonlinear approaches [72; 116; 117; 118; 119]. The SVR and RF techniques were particularly selected in this study to achieve more accurate PM2.5 estimations using satellite-derived AOD, meteorological parameters and gaseous pollutants as predictor variables. The Classification And REgression Training (CARET) package was used to perform the RF and SVR modelling. The data splitting, pre-processing, model tuning and variable importance analysis were executed in a R environment. SVR depends on the kernel function and due to its excellent generalization capability, it is able to minimize the overfitting [120], and therefore, it has been used for PM estimations [69; 108; 121]. SVR can fit the errors within a certain threshold by finding an appropriate boundary line (between hyperplane) to suit the data. The flexibility of SVR depends on the selection of the parameter such as kernel function, cost function and epsilon value. There are four types of kernel functions namely linear, polynomial, sigmoid and radial basis function (RBF) that were used in this study for capturing the non-linear dynamics [69], whilst cost function was used to avoid any overfitting of the data, as small cost value leads to large margin (or wide boundary line) and causes overfitting in the model. The epsilon value controls the number of support vectors used to develop the regression function, while the smaller epsilon value indicates an optimum accuracy. Initially, the SVR parameters are selected based on trial-and-error values, but we found that the default values (Supplementary Materials Table S1) included in the R package \"e1071\" provided the most promising results.  
Random Forest (RF) is a tree-based ML technique proposed by [122]. Theoretically, RF model is an ensemble of multiple decision trees and uses the majority vote/decision of the trees as the final RF model [123; 124]. The algorithm becomes more robust when more decision trees are constructed. RF randomly selects parameters in order to develop each tree, and therefore, it reflects potentially complex effects of predictors on the prediction [125]. The purpose of selecting random predictors instead of all predictors is to reduce the correlation between trees in order to make them disparate [126]. Thus, the variance of the RF prediction can reduce any overfitting. The number of decision trees can be modified to reduce the training time according to a required accuracy and computing capability [127]. In this study, RF model was run using the \"Random Forest\" in the R package. Since, RF is a non-parametric algorithm, here we only set the two most important parameters--although RF can have more parameters--which are mtry and mtree. Parameter mtry is a number of predictors sampled for splitting at each node while ntree is a number of trees in the forest. If mtry value is too small, it might be none of significant parameters included in the subset, and the insignificant parameters would be selected for a split. Therefore, the trees have poor predictive ability [126]. In this study, we set the mtry = 3 (as default: mtry = p/3, where p is the number of parameters used in the model), while ntree is set as 500 in the model. For tuning, we only tune mtry because the CARET package has automatic tuning for _mtry_ only. Therefore, in this study, for ntree, we used the default value [128; 129]. The results were obtained based on best mtry tuning accuracy. It should be mentioned that a limitation of this study is that models were not broadly optimized.