## 1 Introduction  
Many environmental crises currently confront us: global warming, hazardous waste, resource depletion, air pollution, and many more [1; 2; 3; 4]. Millions of people die every year from diseases caused by exposure to outdoor air pollution [5]. In China, the health risk from overexposure to particles is becoming an important public health concern [6]. China's capital, Beijing, has experienced rapid development in economy and energy consumption. Along with this rapid development, hazy weather caused by air pollution has become increasingly serious in Beijing. Air-pollution-weather occurs often and lasts for a long time, although it has seemed better in the last two years [7]. The Air Quality Index (AQI) is an important indicator to reflect and evaluate air quality [8]. According to the Chinese Standard GB3095-2012 [9], AQI is calculated by six major pollutants: fine particulate matter (PM\({}_{2.5}\)), ozone (O\({}_{3}\)), sulfur dioxides (SO\({}_{2}\)), inhalable particles (PM\({}_{10}\)), nitrogen dioxides (NO\({}_{2}\)), and carbon monoxide (CO) [10]. The AQI measures the overall quality of the air on a scale with a range of 0 to 500 that is divided into six levels (good, moderate, lightly polluted, moderately polluted, heavily polluted, and severely polluted); these levels show the impact on human health and provide a good reference for people's outdoor activities in a numerical form [11]. A low number means good air quality, while a higher number means worse air quality, which has ramifications for people's outdoor activities. Governing and solving air pollution problems is a long-term process. Air quality forecasting can help with the prevention of damage caused by air pollution. Therefore, it is necessary for air quality forecasting to occur in a timely manner, to allow government departments and the public to take protective measures and prevent serious pollution incidents. For instance, some plants in Beijing, such as coal-fired power plants and coking plants, have shut down temporarily as a result of the predicted air quality [12]. Machine learning is the scientific study of algorithms and statistical models that computer systems use to make predictions or decisions without being explicitly programmed to perform the task [13]. Machine learning has gained tremendous popularity for its powerful and fast predictions with big data [14]. Big data means enormous datasets, including masses of unstructured data that need more real-time analysis to help us to gain an in-depth understanding of its hidden values [15]. Some researchers have applied machine learning algorithms to the short- and long-term prediction of air quality successfully [16; 17; 18; 19]. [PERSON] et al. predicted the hourly concentration of PM\({}_{2.5}\) in Santiago using a multilayer neural network [20]. Focusing on the problem of poor prediction, authors have discussed using a larger dataset for improvements. [PERSON] et al. proposed two hybrid models (empirical mode decomposition (EMD)-support vector regression (SVR) hybrid and EMD-intrinsic mode functions (IMF) hybrid) to forecast AQI in Xingtai, with the EMD-SVR hybrid model achieving a highest overall accuracy of 80% [11]. However, in the experiment, the authors used only a single indicator (past AQI data) to predict the present AQI, and ignored the correlation between different pollutants (such as PM\({}_{2.5}\), PM\({}_{10}\), and so on). [PERSON] et al. used feed-forward neural networks to predict ozone and PM\({}_{10}\) in Milan [21]. Although the predictions showed a satisfactory reliability, the model still has the tendency toward overfitting, as the authors reported. [PERSON] et al. used a recursive neural network model to forecast PM\({}_{10}\) concentration 1, 2, and 3 days ahead [22]. The recursive neural network model forecasted correctly 95% of the days. However, the percentage of false positives was 30%, which highlights the limits of the neural network model in simulating concentration peaks. [PERSON] et al.