Response to “Comment on ‘Deep Ensemble Machine Learning Framework for the Estimation of ${\mathrm{PM}}_{2.5}$ Concentrations’”

We appreciate the comments by Stafoggia et al.¹ on our article.² We would like to clarify that our article aimed to introduce a novel methodology, deep ensemble machine learning (DEML), to estimate concentrations of air pollutants (e.g., daily, monthly, or annual average concentrations of fine particles, ozone, or nitrogen dioxide). We used Italian data for particulate matter $\le 2.5\mathrm{\mu }\mathrm{g}$ in aerodynamic diameter (${\mathrm{PM}}_{2.5}$) as a practice case to demonstrate how to implement DEML. The estimated concentrations of ${\mathrm{PM}}_{2.5}$ will not be used for epidemiological studies.

We agree that the number of monitoring stations measuring ${\mathrm{PM}}_{2.5}$ in Italy is larger than what we used. One major reason is that, as we stated, we deleted all missing values in the input predictors to reduce the uncertainties involved in interpolation. We included 204 monitoring stations in our original data set; after deleting the missing data, we were left with 133 valid monitoring stations. In addition, we acknowledge that predictions in southern Italy (including the islands of Sicily and Sardinia) may have high uncertainties because of fewer monitoring sites and high spatial variability, which we discussed in our paper as one of the limitations of our analysis.

In general, we agree that model performances, strictly speaking, should be compared independently with the same training and testing data sets, as we did in our analyses. It is better not to compare model performance with different training and testing data sets used in other studies. However, using even a relatively small number of monitors demonstrates the advantages and outstanding performance of DEML, compared with other commonly used single machine learning models, such as gradient boosting machine, support vector machine, random forest, and eXtreme gradient boosting.

As for the lack of some key spatial or spatiotemporal predictors, we agree that those predictors may be helpful for ${\mathrm{PM}}_{2.5}$ estimations. However, our DEML model, with fewer predictors, still achieved high accuracy ($\text{coefficient of determination}=0.87$). From another perspective, this reflects the ability of DEML to capture the complex relationships and spatiotemporal variations between ${\mathrm{PM}}_{2.5}$ and predictors. We believe that, given more monitoring stations and other key predictors, the performance of DEML would be even better.

Refers to https://doi.org/10.1289/EHP11385