Clarifying Relationship between PM2.5 Concentrations and Spatiotemporal Predictors Using Multi-Way Partial Dependence Plots

Abstract

Atmospheric fine particles (PM2.5) have been found to be harmful to the environment and human health. Recently, remote sensing technology and machine learning models have been used to monitor PM2.5 concentrations. Partial dependence plots (PDP) were used to explore the meteorology mechanisms between predictor variables and PM2.5 concentration in the “black box” models. However, there are two key shortcomings in the original PDP. (1) it calculates the marginal effect of feature(s) on the predicted outcome of a machine learning model, therefore some local effects might be hidden. (2) it requires that the feature(s) for which the partial dependence is computed are not correlated with other features, otherwise the estimated feature effect has a great bias. In this study, the original PDP’s shortcomings were analyzed. Results show the contradictory correlation between the temperature and the PM2.5 concentration that can be given by the original PDP. Furthermore, the spatiotemporal heterogeneity of PM2.5-AOD relationship cannot be displayed well by the original PDP. The drawbacks of the original PDP make it unsuitable for exploring large-area feature effects. To resolve the above issue, multi-way PDP is recommended, which can characterize how the PM2.5 concentrations changed with the temporal and spatial variations of major meteorological factors in China.

Predicting the stereoselectivity of chemical reactions by composite machine learning method

“…PDP shows the dependence between the target response (i.e., enantioselectivity) and an input feature of interest, marginalizing over the values of all other input features. Intuitively, we can interpret the partial dependence as the expected enantioselectivity as a function of the input features of interest 35 . The first row shows the partial dependence plots of “H-X-CNu,” “LUMO,” and “C.” The plots show that the features have a linear relationship with predicted enantioselectivity.…”

Predicting THM Formation and Revealing Its Contributors in Drinking Water Treatment Using Machine Learning

“…This inherited feature importance analysis can only assess a feature’s overall importance; however, it cannot explain how different values of an input feature affect THM formation. In contrast, PDPs exhibit a marginal effect of variables on the model target and explicitly show how different values for a particular feature can variate the prediction . Therefore, we applied PDPs to comprehend and visualize the relationship between each input feature and output feature .…”

“…In contrast, PDPs exhibit a marginal effect of variables on the model target and explicitly show how different values for a particular feature can variate the prediction. 83 Therefore, we applied PDPs to comprehend and visualize the relationship between each input feature and output feature. 80 We conducted the SHAP analysis on the RF model to see if other models have a comparable understanding of THM formation mechanisms.…”

Interpretable Machine Learning Approaches for Forecasting and Predicting Air Pollution: A Systematic Review

“…The permutation feature importance (PFI) method was used by Ren et al (2020) and by Shi et al (2023) to explain the estimation of O3 and PM2.5 concentrations, respectively, by assessing the significance of individual features in different algorithms. PFI works by shuffling the values of a single feature while keeping the others constant (Fisher et al, 2018) and measuring the resulting drop in model performance.…”

“…With the growing interest in interpretable machine learning models in recent years (Molnar et al, 2020), researchers have been exploring their application in air pollution predictions, aiming to improve interpretability while maintaining high accuracy (Ahmad et al, 2022;Shi et al, 2023;Yang et al, 2022b;Jovanovic et al, 2023). Given the increasing interest of policymakers in comprehending model decisions and the lack of comprehensive reviews on this topic, there is a clear need for a review that summarizes the use of interpretable machine learning models in the interpretation and explanation of air pollution predictions.…”