Approaching the upper boundary of driver-response relationships: identifying factors using a novel framework integrating quantile regression with interpretable machine learning

doi:10.1007/s11783-023-1676-2

Front. Environ. Sci. Eng.

2023, Vol. 17

Issue (6) : 76 https://doi.org/10.1007/s11783-023-1676-2

RESEARCH ARTICLE

Approaching the upper boundary of driver-response relationships: identifying factors using a novel framework integrating quantile regression with interpretable machine learning

Zhongyao Liang^1,^2,³(

), Yaoyang Xu⁴, Gang Zhao⁵, Wentao Lu^6,⁷, Zhenghui Fu¹(

), Shuhang Wang¹(

), Tyler Wagner⁸

¹. National Engineering Laboratory for Lake Pollution Control and Ecological Restoration, State Environment Protection Key Laboratory for Lake Pollution Control, Chinese Research Academy of Environmental Sciences, Beijing 100012, China
². Fujian Provincial Key Laboratory for Coastal Ecology and Environmental Studies, Xiamen University, Xiamen 361102, China
³. College of the Environment & Ecology, Xiamen University, Xiamen 361102, China
⁴. Key Laboratory of Urban Environment and Health, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen 361021, China
⁵. Department of Global Ecology, Carnegie Institution for Science, Stanford, CA 94305, USA
⁶. Institute of Strategic Planning, Chinese Academy of Environmental Planning, Beijing 100012, China
⁷. The Center for Beautiful China, Chinese Academy of Environmental Planning, Beijing 100012, China
⁸. U.S. Geological Survey, Pennsylvania Cooperative Fish and Wildlife Research Unit, Pennsylvania State University, University Park, PA 16802, USA

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Abstract

● A novel framework integrating quantile regression with machine learning is proposed.

● It aims to identify factors driving observations to upper boundary of relationship.

● Increasing N:P and TN concentration help fulfill the effect of TP on CHL.

● Wetter and warmer decrease potential and increase eutrophication control difficulty.

● The framework advances applications of quantile regression and machine learning.

The identification of factors that may be forcing ecological observations to approach the upper boundary provides insight into potential mechanisms affecting driver-response relationships, and can help inform ecosystem management, but has rarely been explored. In this study, we propose a novel framework integrating quantile regression with interpretable machine learning. In the first stage of the framework, we estimate the upper boundary of a driver-response relationship using quantile regression. Next, we calculate “potentials” of the response variable depending on the driver, which are defined as vertical distances from the estimated upper boundary of the relationship to observations in the driver-response variable scatter plot. Finally, we identify key factors impacting the potential using a machine learning model. We illustrate the necessary steps to implement the framework using the total phosphorus (TP)-Chlorophyll a (CHL) relationship in lakes across the continental US. We found that the nitrogen to phosphorus ratio (N׃P), annual average precipitation, total nitrogen (TN), and summer average air temperature were key factors impacting the potential of CHL depending on TP. We further revealed important implications of our findings for lake eutrophication management. The important role of N׃P and TN on the potential highlights the co-limitation of phosphorus and nitrogen and indicates the need for dual nutrient criteria. Future wetter and/or warmer climate scenarios can decrease the potential which may reduce the efficacy of lake eutrophication management. The novel framework advances the application of quantile regression to identify factors driving observations to approach the upper boundary of driver-response relationships.

Keywords Driver-response Upper boundary of relationship Interpretable machine learning Quantile regression Total phosphorus Chlorophyll a

Corresponding Author(s): Zhenghui Fu,Shuhang Wang

Issue Date: 16 January 2023

Cite this article:

Zhongyao Liang,Yaoyang Xu,Gang Zhao, et al. Approaching the upper boundary of driver-response relationships: identifying factors using a novel framework integrating quantile regression with interpretable machine learning[J]. Front. Environ. Sci. Eng., 2023, 17(6): 76.

URL:

https://academic.hep.com.cn/fese/EN/10.1007/s11783-023-1676-2
https://academic.hep.com.cn/fese/EN/Y2023/V17/I6/76

Fig.1 Flowchart of the proposed methodology framework.

Tab.1 Search space for the four tuned hyperparameters in the random forests model

Fig.2 Quantile regression results (τ = 0.95) for the TP-CHL relationship, representing the estimated upper boundary of TP-CHL relationship. Points are observations. The black line and gray shaded region represent the fitted line and 95% credible intervals, respectively.

Tab.2 Basic statistics of calculated potentials of CHL depending on TP

Fig.3 Variables importance measured by the root mean square error loss from a random forest model based on permutation analysis. Bars charts and box plots show averages and distributions of root mean square error losses across the iterations of the algorithm.

Fig.4 Partial dependence profiles (thick blue lines) showing changes of potential predictions with N?P, PRCP_30, TEMP_30, and TN. For each factor, narrow gray lines are ceteris paribus profiles given a set of observations and the corresponding partial dependence profile is the average of ceteris paribus profiles. Ceteris paribus profiles show how a model’s prediction would change if the value of a single exploratory variable changed (Biecek and Burzykowski 2021). Dots are 100 randomly sampled observations for the profiles calculation. N?P and TN are log₁₀ transformed. Units for PRCP_30, TEMP_30, and TN are mm, °C, and µg/L, respectively.

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[1]	Aifeng Zhai, Xiaowen Ding, Lin Liu, Quan Zhu, Guohe Huang. Total phosphorus accident pollution and emergency response study based on geographic information system in Three Gorges Reservoir area[J]. Front. Environ. Sci. Eng., 2020, 14(3): 46-.

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