Table 2.

${\mathrm{PM}}_{2.5}$ prediction performances of DEML model and five benchmark models from 2015 to 2019 in Italy.

Year	Measurement	GBM	SVM	RF	XGBoost	SLa	DEMLb
2015	$R^2$	0.69	0.79	0.85	0.81	0.85	0.89
	RMS E (${\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$)	9.25	6.42	6.49	7.23	6.47	5.54
2016	$R^2$	0.72	0.80	0.84	0.81	0.84	0.87
	RMSE (${\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$)	7.74	6.51	5.84	6.33	5.82	5.18
2017	$R^2$	0.74	0.81	0.85	0.81	0.85	0.89
	RMSE (${\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$)	8.20	7.19	6.41	7.09	6.38	5.37
2018	$R^2$	0.70	0.78	0.86	0.82	0.86	0.89
	RMSE (${\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$)	7.44	6.22	5.18	5.69	5.13	4.43
2019	$R^2$	0.68	0.76	0.84	0.79	0.84	0.87
	RMSE (${\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$)	7.34	6.42	5.13	5.78	5.12	4.55
Total	$R^2$	0.51	0.76	0.83	0.70	0.83	0.87
	RMSE (${\mathrm{\mu }\mathrm{g}/\mathrm{m}}^3$)	10.4	7.42	6.23	8.20	6.23	5.38

Note: DEML, the three-stage stacked deep ensemble machine learning method; GBM, gradient boosting machine; ${\mathrm{PM}}_{2.5}$, particulate matter with aerodynamic diameter $<2.5\mathrm{\mu }\mathrm{m}$; $R^2$, coefficients of determination for unseen independent data; RF, random forest; RMSE, root mean square error; SL, super learner algorithm; SVM, support vector machine; XGBoost, extreme gradient boosting.

^a SL was constructed with four machine learning models (GBM, SVM, RF, and XGBoost) using a nonnegative least squares (NNLS) approach to achieve the optimal weight.

^b DEML was a three-stage stacked ensemble model by constructing with four base models (GBM, SVM, RF, and XGBoost), three second-level models (RF, XGBoost, and GLM), and an NNLS algorithm.