Deep Ensemble Machine Learning Framework for the Estimation of PM2.5 Concentrations

Abstract

Background: Accurate estimation of historical ${\mathrm{PM}}_{2.5}$ (particle matter with an aerodynamic diameter of less than $2.5\mu m$) is critical and essential for environmental health risk assessment.

Objectives: The aim of this study was to develop a multiple-level stacked ensemble machine learning framework for improving the estimation of the daily ground-level ${\mathrm{PM}}_{2.5}$ concentrations.

Methods: An innovative deep ensemble machine learning framework (DEML) was developed to estimate the daily ${\mathrm{PM}}_{2.5}$ concentrations. The framework has a three-stage structure: At the first stage, four base models [gradient boosting machine (GBM), support vector machine (SVM), random forest (RF), and eXtreme gradient boosting (XGBoost)] were used to generate a new data set of ${\mathrm{PM}}_{2.5}$ concentrations for training the next-stage learners. At the second stage, three meta-models [RF, XGBoost, and Generalized Linear Model (GLM)] were used to estimate ${\mathrm{PM}}_{2.5}$ concentrations using a combination of the original data set and the predictions from the first-stage models. At the third stage, a nonnegative least squares (NNLS) algorithm was employed to obtain the optimal weights for ${\mathrm{PM}}_{2.5}$ estimation. We took the data from 133 monitoring stations in Italy as an example to implement the DEML to predict daily ${\mathrm{PM}}_{2.5}$ at each $1\mathrm{km}\times 1\mathrm{km}$ grid cell from 2015 to 2019 across Italy. We evaluated the model performance by performing 10-fold cross-validation (CV) and compared it with five benchmark algorithms [GBM, SVM, RF, XGBoost, and Super Learner (SL)].

Results: The results revealed that the ${\mathrm{PM}}_{2.5}$ prediction performance of DEML [coefficients of determination $\left(R^2\right)=0.87$ and root mean square error $\left(\text{RMSE}\right)=5.3{8\mu g/m}^3$] was superior to any benchmark models (with $R^2$ of 0.51, 0.76, 0.83, 0.70, and 0.83 for GBM, SVM, RF, XGBoost, and SL approach, respectively). DEML displayed reliable performance in capturing the spatiotemporal variations of ${\mathrm{PM}}_{2.5}$ in Italy.

Discussion: The proposed DEML framework achieved an outstanding performance in ${\mathrm{PM}}_{2.5}$ estimation, which could be used as a tool for more accurate environmental exposure assessment. https://doi.org/10.1289/EHP9752.

Figure 1.

The framework of the DEML algorithm. $Z_1$ is a matrix with $n$ rows and $m$ columns, which is the combination of ${\mathrm{PM}}_{2.5}$ predictions for each base model; l represents the original features; h denotes the number of meta-models; $Z_2$ is a matrix with $n$ row and $h$ columns, which is the combination of ${\mathrm{PM}}_{2.5}$ predictions for each meta model. We finally get $Z_2$ as the input to obtain the weights of the meta models by using the NNLS algorithm and get the final ${\mathrm{PM}}_{2.5}$ prediction; k is the number of folds for CV, and we select the same valid rows for the base and meta models; $n$ is the number of records of all data; $m$ denotes the number of base models. Note: CV, cross-validation analysis; DEML, the three-stage stacked deep ensemble machine learning method; GBM, gradient boosting machine; GLM, generalized linear model; NNLS, nonnegative least squares algorithm; RF, random forest; SVM, support vector machine; XGBoost, extreme gradient boosting.

Figure 2.

The ${\mathrm{PM}}_{2.5}$ prediction performance of the DEML model in different seasons of 2015–2019 in Italy. The x-axis indicates the observed daily ${\mathrm{PM}}_{2.5}$ in the monitor stations; y-axis indicates the estimated ${\mathrm{PM}}_{2.5}$ by the DEML model; the points represent the corresponding ${\mathrm{PM}}_{2.5}$ for both observed and predicted values. The solid line represents a regression line for the observed and predicted ${\mathrm{PM}}_{2.5}$ by using the simple linear regression. $R^2$ is the coefficients of determination for the unseen independent data. (A) Overall performance. (B) Spring means from March to May; (C) Summer means from June to August; (D) Autumn means from September to November; and (E) Winter means from December to February. Note: DEML, the three-stage stacked deep ensemble machine learning method; ${\mathrm{PM}}_{2.5}$, particulate matter with an aerodynamic diameter $<2.5\mathrm{\mu }\mathrm{m}$; RMSE, the root mean square error (micrograms per cubic meter).

Figure 3.

The estimated annual average concentrations of particulate matter with an aerodynamic diameter $<2.5\mathrm{\mu }\mathrm{m}$ (${\mathrm{PM}}_{2.5}$) (micrograms per cubic meter) from 2015 to 2019 in Italy at $1\mathrm{km}\times 1\mathrm{km}$ spatial resolution.

Figure 4.

The ${\mathrm{PM}}_{2.5}$ prediction performance of the DEML models with and without AOD as a predictor from 2015–2019 in Italy. The x-axis indicates the observed daily ${\mathrm{PM}}_{2.5}$ in the monitor stations; the y-axis indicates the estimated ${\mathrm{PM}}_{2.5}$ by the DEML model. The points represent the corresponding ${\mathrm{PM}}_{2.5}$ for both observed and predicted values. The solid line represents a regression line for the observed and predicted ${\mathrm{PM}}_{2.5}$ by using the simple linear regression. $R^2$ is the coefficients of determination for the unseen independent data. (A) The DEML prediction model including AOD. (B) The DEML prediction model without AOD. Note: DEML, the three-stage stacked deep ensemble machine learning method; ${\mathrm{PM}}_{2.5}$, particulate matter with aerodynamic diameter $<2.5\mathrm{\mu }\mathrm{m}$; RMSE, the root mean square error (micrograms per cubic meter).