## 2 Related Work and Contributions  
### Related Work  
We have performed a comprehensive review of recent work on PM\({}_{2.5}\) forecasting. Current forecasting approaches can be classified into the following five categories. (1) _Regression or autoregression. First,_ regression (either linear or nonlinear) techniques stem from a set of explanatory variables (such as meteorological metrics, traffic conditions, road types, etc.) and use them to estimate the response variable (i.e., PM\({}_{2.5}\) concentrations) by training on cross-sectional data. Regression techniques are useful for analyzing the relationship between explanatory variables and the response variable. However, the selection of effective explanatory variables depends on the local meteorological patterns and it is critical to the prediction accuracy. Multivariate linear regression models for the forecasting of concentrations of NOx and PM\({}_{10}\) in Athens and Helsinki have been intensively evaluated by [12] using NO, NO\({}_{2}\), CO, O\({}_{3}\), and PM\({}_{2.5}\) as the explanatory variables. Nonlinear regression models have been deployed in [13] to forecast the PM\({}_{2.5}\) air quality and detect unhealthy PM\({}_{2.5}\) event in the Louisville, Kentucky metropolitan area. Separate nonlinear regression models were presented by [14] for primary PM\({}_{2.5}\), PM\({}_{2.5}\) sulfate ion, and PM\({}_{2.5}\) nitrate ion. The explanatory variables of the nonlinear regression models included facility emissions rates in tons per year and the distance between the single emissions source and receptor. The multiple nonlinear regressions were found useful in predicting Beijing's daily PM\({}_{2.5}\) concentration with one nonlinear regression applied to each season of meteorological conditions [15]. The graphically and temporally weighted regression has been attempted in [16] to find the relationship between the surface PM\({}_{2.5}\) concentration and the satellite-derived aerosol optical depth (AOD) data. Dynamic multiple linear equations have been used in [17] to model the hourly PM\({}_{2.5}\) concentration in relation to meteorological characteristics. The authors showed that the prediction accuracy of the dynamic system could surpass to that obtained by nonlinear models. A spatiotemporal land use regression method was applied to forecast the PM\({}_{2.5}\) concentration in finely-grained spatial grids [18]. The result showed that the PM\({}_{2.5}\) concentration level in primary schools is significantly different to the mean PM\({}_{2.5}\) level of the corresponding city. Second, autoregression methods, such as autoregressive integrated moving average model (ARIMA) and generalized autoregressive conditional heteroscedasticity (GARCH), require no explanatory variables but focus on discovering the temporal trends contained in the PM\({}_{2.5}\) time series. ARIMA was adopted in [19] to explore the short-term time series and estimate the mean daily PM\({}_{2.5}\) concentration. A GARCH model was used in [8] to capture linear and nonlinear panel information for PM\({}_{2.5}\) concentrations forecasting. (2) _Machine learning._ Machine learning approaches are the main stream in the literature of PM\({}_{2.5}\) forecasting. The approaches, such as artificial neural networks (ANNs), fuzzy systems, and support vector machine (SVM), are able to learn the relationship function between the explanatory variables and the responsive variable (PM\({}_{2.5}\) concentrations) based on training data. The advantage of machine learning is that there is no prior assumption for the form of the relationship function. In other words, a black-box learning is implicitly performed without the need to anticipate the analytic form of the relationship. General regression neural networks (GRNN) have been applied in [20] to predict all decomposed PM\({}_{2.5}\) components obtained by the ensemble empirical mode decomposition (EEMD) method.