University of Southern California Dissertations and Theses

Uncertainty quantification in extreme gradient boosting with application to environmental epidemiology

(USC Thesis Other)

Uncertainty quantification in extreme gradient boosting with application to environmental epidemiology

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content Uncertainty Quantification in Extreme Gradient Boosting with Application to Environmental Epidemiology by Xiaozhe Yin A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (BIOSTATISTICS) December 2022 Copyright 2022 Xiaozhe Yin Dedication To my mom, Xiangwei. ii Acknowledgements I would like to thank my dissertation committee members who are more than generous with their expertise and precious time. Dr. Yao-Yi Chiang has always been encouraging and he taught me how to use PostgreSQL, which made the data management part of my research much easier and more manageable. He also helped me edit my Association of Pacific Coast Geographers con- ference paper, which won the Geosystems Award. Dr. Juan Pablo Lewinger provided insightful ideas in terms of model optimization and epidemiological analysis accounting for uncertainty. Dr. Rob McConnell and Dr. Scott Fruin have witnessed every step of my growth since I joined the program and provided thoughtful suggestions and feedback on my work even though some did not make it into the final form of the dissertation. Deepest gratitude to my advisor, Dr. Meredith Franklin, who took me on as a student when things were most difficult for me. She has been a tremendous mentor, colleague, and friend. All of my achievements would not have been possible without her. I feel extremely lucky to have her as my advisor and I will always be grateful for that. I am also grateful to Dr. Travis Longcore who introduced me to light pollution. I still remem- ber the nights our group went to the coast of southern California to measure illuminance. It has been an honor to work with him and the team even for a short time period. I thank Dr. Kimberly Siegmund, who gave me the opportunity to teach spatial statistics for the LA’s BEST summer iii program and gave me support for my dissertation defense and postdoc application. My sincere thanks to Masoud, whom I have been enjoying working, hiking, and playing sports with during the past three years. I thank Richard and his wife May, who have been like family to me and invited me for dinner every Independence Day and Thanksgiving for the past 5 years. I would like to thank my dear friends Wanting, Emily, Kate, Lois, Johanna, Yan, Weiwei, and Yijun, who gave me a lot of love, comfort, and support in this journey. I will always remember the joys and tears we shared together. I also acknowledge my gratitude to my Soto colleagues and friends, Menglin, Charlie, Ken and many others that I did not list the names of here for their help and friendship along the road. Finally, I give special thanks to Derek, for always being there for me and his faithful support during the past two years. I am grateful for all the unconditional love from my family in China, especially my mom Xiangwei, whose support, encouragement, and constant love have sustained me throughout my life. She is by far the strongest woman I have ever known. I dedicate this to you, my mom. iv TableofContents Dedication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Machine Learning in Environmental Science . . . . . . . . . . . . . . . . . . . . . 1 1.2 Uncertainty Construction Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Bayesian Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 Delta Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.3 Bootstrap Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.4 Lower Upper Bound Estimation Method . . . . . . . . . . . . . . . . . . . 7 1.2.5 Quantile Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.6 Summaries of Prediction Intervals Construction Methods . . . . . . . . . . 9 1.3 Prediction Intervals in GBM, LightGBM, and XGBoost . . . . . . . . . . . . . . . . 10 1.3.1 Gradient Boosting Machine . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.2 Light Gradient Boosting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.3 Extreme Gradient Boosting . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4 Knowledge Gaps and Significance of the Study . . . . . . . . . . . . . . . . . . . . 15 1.5 Summaries of Each Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Chapter 2: Predicting Fine Spatial Scale Traffic Noise Using Mobile Measurements and Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.1 Traffic Noise and Health . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.2 Noise Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.3 Mobile Noise Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.1 Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.2 Traffic Noise Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 v 2.2.3 Road Features Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2.4 Land Use Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.5 Traffic Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.6 Meteorological Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.2.7 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.2.8 Model Training and Validation . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.2.9 Traffic noise prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3.1 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3.2 Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.3.3 Prediction Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.5 Supplementary Tables and Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Chapter 3: Uncertainty Quantification in Extreme Gradient Boosting Using Quantile Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1 Mathematics in Extreme Gradient Boosting . . . . . . . . . . . . . . . . . . . . . . 53 3.2 Mathematics in Quantile Regression . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.3 Quantile Extreme Gradient Boosting . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3.1 Challenges of Using Quantile Regression as the Objective Function . . . . 62 3.3.2 Smoothing Approximation of Quantile Regression . . . . . . . . . . . . . . 63 3.4 Evaluations of Prediction Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.5 Experiments and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5.1 Experiment on Simulated Data . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5.2 Experiment on Traffic Noise Data . . . . . . . . . . . . . . . . . . . . . . . 74 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Chapter 4: The Role of Traffic Noise on the Association Between Air Pollution and Children’s Lung Function After Accounting for Uncertainty . . . . . . . . . . 82 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2 Material and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.2.1 Study Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.2.2 Health Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.2.3 Environmental Exposures . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.2.3.1 Air Pollution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.2.3.2 Traffic Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.2.4 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.3.1 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.3.2 Main Analyses Without Uncertainty . . . . . . . . . . . . . . . . . . . . . 94 4.3.3 Main Analyses With Uncertainty . . . . . . . . . . . . . . . . . . . . . . . 96 4.4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Chapter 5: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 vi 5.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.3 Future Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 vii ListofTables 2.1 Summary statistics of traffic noise and leave-one-route-out CV R 2 and RMSE for different routes across all models. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.2 Relative contribution (RC) of predictor variables (top ten) in all models. . . . . . . 41 2.3 Description of machine learning and tuning parameters. . . . . . . . . . . . . . . 47 2.4 Model comparisons between “Pseudo-fixed site” and mobile monitoring approaches. 48 3.1 Hyperparameter tuning for simulated data. . . . . . . . . . . . . . . . . . . . . . . 71 3.2 Prediction interval results for the toy data. . . . . . . . . . . . . . . . . . . . . . . 72 3.3 Hyperparameter tuning for the traffic noise data. . . . . . . . . . . . . . . . . . . 75 3.4 Prediction interval results for the traffic noise data. . . . . . . . . . . . . . . . . . 75 4.1 Characteristics of the study population . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2 Pearson correlation coefficients for environmental risk factors . . . . . . . . . . . 93 4.3 Estimated linear associations between FEV 1 and environmental factors from unadjusted and adjusted models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.4 Estimated linear associations between FVC and environmental factors from unadjusted and adjusted models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.5 The mean and SD of the traffic noise coefficients from single exposure models based on different numbers of simulations . . . . . . . . . . . . . . . . . . . . . . 96 4.6 The mean and SD of air pollution coefficients from single exposure models based on different numbers of simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 98 viii ListofFigures 1.1 The relationships and connections among three projects from chapter 2, 3, and 4. 17 2.1 Study area of Long Beach, California (for display purposes tertiary and service roads are not shown). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Average daily traffic volumes on Long Beach, California motorways is based on Caltrans AADT sensor measurements. Red lines represent periods of relatively flat volumes during our study period. . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3 OSM data extraction flow chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 Traffic volume simulation flow chart (the reference databases are represented in parentheses). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5 Traffic volume in Long Beach, California simulated by SUMO. . . . . . . . . . . . 29 2.6 Data processing flow diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.7 Correlation heatmap of the 20 most important variables from extreme gradient boosting, constructed by a hierarchical clustering tree, which shows that the correlation between the variables are both positive and negative and high, ranging from - 0.83 to 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.8 Traffic noise map with labeled route numbers (circled). For display purposes, we only show here a random 30% selection of the traffic noise points. . . . . . . . . . 36 2.9 Cross-validation results for predicting 20 m LAeq using a: Linear Regression, b: Neural Network, c: Random Forest, d: Extreme Gradient Boosting. Solid lines represent the regression line, and dashed lines represent the 1:1 correspondence between measured and predicted values. . . . . . . . . . . . . . . . . . . . . . . . 38 2.10 Prediction of traffic noise from a: Linear Regression, b: Neural Network, c: Random Forest, and d: Extreme Gradient Boosting. . . . . . . . . . . . . . . . . . 43 ix 2.11 “Pseudo-fixed site” results for predicting 20 m LAeq using a: Linear Regression, b: Neural Network, c: Random Forest, d: Extreme Gradient Boosting. Solid lines represent the regression line, and dashed lines represent the 1:1 correspondence between measured and predicted values. . . . . . . . . . . . . . . . . . . . . . . . 48 2.12 Leave-one-route-out Cross-validation results for predicting route 12 LAeq using Linear Regression, Neural Networks, Random Forests, and Extreme Gradient Boosting. The left figures present the predicted LAeq; the right figures present the corresponding residuals plots. All prediction maps are plotted at the same color scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.13 Leave-one-route-out Cross-validation results for predicting route 10 LAeq using Linear Regression, Neural Network, Random Forest, and Extreme Gradient Boosting. The left figures present the predicted LAeq; the right figures present the corresponding residuals plots. All maps are plotted with the same color scale. 52 3.1 Ensemble tree withn additive base learners. . . . . . . . . . . . . . . . . . . . . . 54 3.2 Structure score calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3 Greedy search process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4 Quantile plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.5 The difference between the absolute value function and Huber function with different thresholds when the quantile τ = 0.90. . . . . . . . . . . . . . . . . . . . 65 3.6 First and second derivatives of the proposed loss function. . . . . . . . . . . . . . 67 3.7 Comparison of prediction intervals for the toy data using three methods. The dark blue dots are the observations. The red lines are the point predictions of the traffic noise. The two black lines represent the upper and lower bounds of the PIs and the blue areas in between are the PIs. . . . . . . . . . . . . . . . . . . . . . 73 3.8 Point prediction for traffic noise using GBM, LightGBM, and XGBoost. Blue points represent each observed and predicted sample; solid red lines represent the regression line; and dashed black lines represent the 1:1 correspondence between measured and predicted values. . . . . . . . . . . . . . . . . . . . . . . . 74 3.9 PIs for the traffic noise data from all three models. The turquoise lines represent the PIs. The orange points are the point predictions of the traffic noise. The figures on the first row are the PIs for the test set. The figures on the second row are the PIs for 20 randomly selected points. . . . . . . . . . . . . . . . . . . . . . . 77 x 3.10 Ordered and centered PIs for the traffic noise data from all three models. The orange dots represent the observations that are covered by PIs. The turquoise dots are the observations that are not covered by PIs. The blue areas show the ordered and centered PIs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.11 Ordered and centered PIs from all three models on the same plot. QGBM is quantile GBM, LGBM is quantile LightGBM, and QXGB is quantile XGBoost. . . . 79 4.1 Uniform and Gaussian sampling methods . . . . . . . . . . . . . . . . . . . . . . . 89 4.2 Selected environmental exposures . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.3 The coefficients and confidence interval distributions of PM 2.5 for FEV 1 after accounting for traffic noise with uncertainty. . . . . . . . . . . . . . . . . . . . . . 99 4.4 The coefficients and confidence interval distributions of PM 2.5 for FVC after accounting for traffic noise with uncertainty. . . . . . . . . . . . . . . . . . . . . . 100 4.5 The coefficients and confidence interval distributions of freeway NO x for FEV 1 after accounting for traffic noise with uncertainty. . . . . . . . . . . . . . . . . . . 101 4.6 The coefficients and confidence interval distributions of freeway NO x for FVC after accounting for traffic noise with uncertainty. . . . . . . . . . . . . . . . . . . 102 4.7 The coefficients and confidence interval distributions of non-freeway NO x for FEV 1 after accounting for traffic noise with uncertainty. . . . . . . . . . . . . . . . 103 4.8 The coefficients and confidence interval distributions of non-freeway NO x for FVC after accounting for traffic noise with uncertainty. . . . . . . . . . . . . . . . 104 xi Abstract Environmental noise has been associated with a variety of health endpoints including cardio- vascular disease, sleep disturbance, depression, and psychosocial stress. Most population noise exposure comes from vehicular traffic, which has large fine-scale spatial variability that is dif- ficult to characterize using traditional fixed-site measurement techniques. To address this chal- lenge, we collected A-weighted, equivalent noise (LAeq in decibels, dB) data on hour-long foot journeys around 16 locations throughout Long Beach, CA, and trained four machine learning models, linear regression, random forest, extreme gradient boosting, and a neural network, to predict noise with 20 m resolution. Input variables to the models included traffic metrics, road network features, meteorological conditions, and land use types. Among all machine learning models, extreme gradient boosting had the best results in validation tests (leave-one-route-out R 2 = 0.71, root mean square error (RMSE) 4.54 dB; 5-fold R 2 = 0.96, RMSE 1.8 dB). Local traffic volume was the most important predictor of noise; road features, land use, and meteorology in- cluding humidity, temperature, and wind speed also contributed. We show that a novel, on-foot mobile noise measurement method coupled with machine learning approaches enables highly ac- curate predictions of small-scale spatial patterns in traffic-related noise over a mixed-use urban area. xii Estimating uncertainty in exposure model predictions is an underutilized but potentially im- portant metric in environmental epidemiological studies. Failure to account for uncertainty can lead to biased results in exposure-response analyses. Given the recent popularity of machine learning methods such as Extreme Gradient Boosting (XGBoost) for exposure modeling, where uncertainty determinations are still not standardized, uncertainty analysis is an area deserving of greater attention. We propose enhancements to XGBoost whereby a modified quantile regression is used as the objective function in order to estimate uncertainty (QXGBoost). Specifically, we included the Huber norm in the quantile regression model to construct a differentiable approx- imation to the quantile regression error function. This key step allows the gradient-based opti- mization algorithm in XGBoost to make probabilistic predictions more efficiently and improve the efficiency of finding the optimal gradient descent rates for rapid solutions. These techniques were then applied to create 90% prediction intervals for one simulated dataset and a real-life environmental dataset of measured traffic noise. For both datasets, QXGBoost had better model performance compared to regular quantile gradient boosting and quantile light gradient boosting. In the test datasets, almost 90% of the observations lay within the prediction intervals using QXGBoost. For the simulated and traffic noise datasets, the quality of the prediction intervals from QXGBoost was better than the other models. Thus, compared to other methods, our prediction intervals using QXGBoost show better performance metrics. Uncertainty estimates of traffic noise, central site PM 2.5 , and freeway and non-freeway emis- sion concentrations of oxides of nitrogen (NO x , ppb) were spatially assigned to children in Long Beach who were tested for forced vital capacity (FVC) and forced expiratory volume in 1 sec- ond, (FEV 1 ). The associations between traffic related air pollution and these outcomes, with and xiii without adjustment for noise, were examined using mixed effects models. To account for the uncertainties of traffic noise, different numbers of intensive simulations were drawn within the lower and upper bound of the prediction intervals using both uniform and Gaussian sampling methods. The generated traffic noise variables were then fit iteratively in the mixed effects mod- els to examine their average effect on the associations between traffic-related air pollution and lung function (represented by FEV 1 and FVC). Overall, traffic noise with or without uncertainty did not confound the association between PM 2.5 and lung function. Traffic noise without uncer- tainty confounded 36.0% and 18.3% of the association between freeway NO x and FEV 1 and FVC, respectively, and 59.2% and 62.9% for non-freeway NO x . After accounting for uncertainty, the confounding effects were reduced to 14% and 6.7% between freeway NO x and FEV 1 and FVC, and 31.4% and 34.1% between freeway NO x and FEV 1 and FVC. The confounding effect of traffic noise is diminished after accounting for uncertainty. Our results indicated that failure to account for uncertainties in exposure estimation may lead to underestimation of the effect of exposures in epidemiological studies. Gaussian sampling methods could give results closer to those without accounting for uncertainty. Usually, a large number of simulations could give better and more robust results, but it also depends on the data. xiv Chapter1 Introduction In this chapter we reviewed the application of machine learning models in the area of environ- mental science, summarized commonly used methods for uncertainty analysis, as well as the pros and cons of each method. We then focused on three tree based boosting methods, including gradient boosting machines (GBM), Light Gradient Boosting Machine (LightGBM), and Extreme Gradient Boosting (XGBoost), and explored the uncertainty quantification in GBM and Light- GBM. Finally, we identified the gap between XGBoost and uncertainty analysis that motivated our proposed method. 1.1 MachineLearninginEnvironmentalScience During the past few decades, the environment has been subjected to detrimental anthropogenic activities, and as a result, mankind has been faced with unprecedented challenges imposed by the environment [75], among which, air pollution and noise pollution ranked as the top two most important environmental burdens of disease risk factors [64]. Numerous studies have established the adverse health outcomes, and the increasing mortality and morbidity caused by both air and 1 noise pollution [71, 62, 14]. Thus, monitoring, modeling, and assessing environmental risk factors can help us better understand how human activities affect the environment and equip us with knowledge to deal with environmental issues. One of the great challenges that comes with environmental science is the ’big data’ issue. Environmental data are usually extracted from different sources that are extremely diverse in nature, which make datasets too large and complex to be dealt with by traditional data processing, analysing, and modeling techniques [98]. As a result, machine learning (ML) methods, which are well known to deal with heterogeneous data and have less dependence on prior knowledge and assumptions of data, have been widely adopted in environmental science to integrate, analyze, and solve complex data related problems [162]. For example, ML methods have been used in environmental monitoring [68, 72], risk assessment [76], spatial interpolation [91], modeling [99], and predictions [157]. The most widely used ML models in environmental epidemiology include decision trees, Bayesian methods, support vector machines, and artificial neural networks [7]. Despite the broad applications, few studies have explored the uncertainty analysis in ML models. 1.2 UncertaintyConstructionMethods Many environmental and scientific problems such as climate change, global warming, air pollu- tion, and marine activity related issues are difficult to define and quantify because they consist of both deterministic and random situations. The modeling results of these problems cannot be sim- ply determined by a classification problem with true or false or a regression problem with point predictions. Even though the traditional ML models such as gradient boosting algorithms and neural networks have achieved state-of-the-art performance in deterministic point predictions, 2 these predictions have been shown to be miscalibrated and tend to yield arbitrarily high con- fidence [59]. Predictions without uncertainty quantification cannot provide information about their reliability. In general, there are two types of uncertainties one can model. One is aleatoric uncertainty and the other is epistemic uncertainty [3]. Aleatoric uncertainty is the inherent prop- erty of the data and it is considered irreducible. Epistemic uncertainty is the introduced uncer- tainty during the modeling process that can be assessed using appropriate uncertainty quantifi- cation methods. Prediction intervals (PIs) have been considered as a powerful way of quantifying the model uncertainty associated with predictions to overcome the limitations of point predic- tion [100], especially in the deep learning area. The commonly used uncertainty quantification methods include Bayesian, Delta, bootstrap, lower and upper bound estimation, and quantile regression methods. 1.2.1 BayesianMethod The Bayesian neural network or Bayesian deep learning, an application of the Bayesian method in the deep learning area, has been widely studied. The traditional neural network methods are trained to minimize the objective function and obtain the optimal weights. Instead, the Bayesian neural network attempts to train the traditional neural network to optimize the posterior prob- ability distribution of weights by a predefined prior distribution [74, 111]. Mathematically, the Bayesian neural network can be written as [81] P(w|D,ρ,β,M ) = P(D|w,ρ,M )P(w|ρ,M ) P(D|ρ,β,M ) (1.1) 3 where w is a random set of variables with predefined distribution. ρ and β are the parameters that use to determine training goals.M represents the neural network model andD refers to the training dataset. P(D|w,ρ,M ) is the likelihood function. P(w|ρ,M ) denotes the prior density of parameters. P(D|ρ,β,M ) is a normalized factor that guarantees the total probability is 1. The Bayesian neural network can model both the aleatoric and epistemic uncertainties. Thus, the total variance σ 2 i that corresponds to both the data and parameters in the Bayesian neural network method was expressed as [81] σ 2 i = 1 β +∇ T w MP ˆ y i (H M P) − 1 ∇ w MPˆ y i (1.2) where∇ T w MP ˆ y i refers to the neural network output gradient with respect to its parametersw MP . H MP is the Hessian matrix of the sum of squares of the network weightsE(w) H MP =ρ ∇ 2 E w +β ∇ 2 E D (1.3) For thei t h sample, the(1− α )% PI can be obtained by [81] PI = ˆ y i ± z 1− α 2 ( 1 β +∇ T w MP ˆ y i (H MP ) − 1 ∇ w MPˆ y i ) 1 2 (1.4) wherez 1− α 2 is the1− α 2 quantile of the normal distribution function with 0 mean and unit vari- ance. The Bayesian method can usually be easily generalized to other machine learning methods, for example, the Bayesian additive regression trees, which mimics gradient boosting tree methods [29], and Bayesian random forest [117]. However, the application of the Bayesian method requires strong mathematical knowledge and statistical expertise and the inference in the Bayesian neural 4 network method requires the calculation of the Hessian matrix, which is a very computationally expensive approximation process, especially for large datasets. All these limits the ease-of-use of the Bayesian method. 1.2.2 DeltaMethod In statistics, the Delta method approximates non-normal functions to an asymptotically normal distribution by using the Taylor series expansion theory. In the context of combining the delta method and neural networks, the parameters of the neural network model are optimized by min- imizing the error-based cost function. Then, the Delta asymptotic theory is applied to construct PIs for the models [125]. In the Delta method, the total variance of a Markov decision process is represented as [81] σ 2 0 =σ 2 ϵ (1+g T 0 (J J J T J J J) − 1 )g 0 ) (1.5) whereJ is the Jacobian matrix of the neural network model andσ 2 ϵ represents the unbiased mean square error that can be calculated as σ 2 ϵ = 1 n− 1 n X i=1 (y i − ˆ y i ) (1.6) Here,y i is thei th observed target value. If the distribution is assumed as a Gaussian distribution, then the(1− α )% PI for ˆ y i can be written as [70] PI = ˆ y 0 ± t 1− α 2 n− p σ ϵ (1+g T 0 (J J J T J J J) − 1 )g 0 ) 1 2 (1.7) 5 wheret 1− α 2 n− p is the1− α 2 quantile of a cumulative distribution function withn− p degrees of free- dom. One of the biggest limitations in the Delta method is that the data distribution is assumed to be Gaussian and the variances are assumed to be normally distributed and homogeneous, which is not very practical as the the real life data are almost always heterogeneous. Thus, the Delta method cannot produce very satisfying results for some occasions. Additionally, the Delta method involves the calculation of the Jacobian matrix (J J J) andσ 2 0 , which makes it very compu- tationally intensive and the calculation of the gradient and the Jacobian matrix in equation 1.7 can be potential sources of error [139]. 1.2.3 BootstrapMethod Bootstrap is a statistical technique for estimating quantities about a population by averaging from multiple small data samples. It is also a very important and commonly used technique for uncertainty analysis, where the method assembles several models, for example, neural networks, to construct PIs [164, 37]. The randomly selected samples from the data are used for training each of the neural networks, the results of which would lead to lower estimation errors compared to a single neural network. The mean and variance of each neural network model from the bootstrap estimation can be calculated as follows [111] ˆ y i (x) = 1 B B X b=1 f b i (x) σ 2 ˆ y i = 1 B− 1 B X b=1 (f b i (x)− ˆ y i (x)) 2 (1.8) 6 where ˆ y i (x) is the prediction of the i th sample obtained from the b th neural network bootstrap modelf b i . Based on equation 1.8, PIs (for example(a,b)) can be calculated as P(a<X υ (3.20) where the threshold υ is a positive real number. By replacing the error x in the absolute value function 3.16 with the Huber function 3.20, we get ρ τ =                              (τ − 1)(|t|− υ 2 ) t<− υ (τ − 1)( t 2 2υ ) − υ ≤ t< 0 τ ( t 2 2υ ) 0≤ t<υ τ (|t|− υ 2 ) t>υ (3.21) Equation 3.21 is our proposed loss function for QXGBoost to construct PIs. Figure 3.5 shows the comparison between the original absolute value function and the Huber smoothed absolute value function with different thresholds when the quantile τ = 0.90. As we can see, the Huber smoothed absolute value function h υ (t) is continuously differentiable and provides a smooth transition between absolute and square errors around the origin [20]. When the threshold is small (υ is less than 2), the Huber smoothed absolute value function approximates the absolute value function really well. As the thresholdυ gets larger, the Huber smoothed absolute value function departs further away from the original absolute value function. Thus, in practice, smallerυ values are preferred. 64 Figure 3.5: The difference between the absolute value function and Huber function with different thresholds when the quantileτ = 0.90. 65 The first and second derivatives of our proposed loss function in equation 3.21 are presented in equation 3.22 and 3.23, respectively. ∇ ρ =                              (1− τ ) t<− υ (τ − 1)( t υ ) − υ ≤ t< 0 τ ( t υ ) 0≤ t<υ τ t>υ (3.22) ∇ 2 ρ =                              0 t<− υ τ − 1 υ − υ ≤ t< 0 τ υ 0≤ t<υ 0 t>υ (3.23) Figure 3.6 shows the first and second derivatives of the proposed loss function. We can see that, the first derivative is not 0 everywhere, but the second derivative has non-zero values only be- tween− υ andυ . Both the first and second derivatives are confined in the value between -1 and 1. Our proposed objective function meets the requirements of having first and second derivatives exist and not all 0. To sum up, inspired by the idea of quantile neural networks, GBM, LightGBM, and random forest, we came up with the idea of combining quantile regression with XGBoost for the latter to do uncertainty analysis. For the quantile regression function to be a qualified objective function (have first and second derivatives everywhere in the defined sample space and not all 0), we 66 Figure 3.6: First and second derivatives of the proposed loss function. 67 introduced the Huber smoothed absolute value function, which is a differentiable approximation to the absolute value function that provides a smooth transition between absolute and squared errors around the origin. Accordingly, we have two sets of parameters that need to be tuned for QXGBoost. One set of parameters are inhabited in the XGBoost model, the most important parameters of which include the number of estimators, the maximum tree depth, and the learning rate. The other set comes with the threshold parameter in the Huber function (υ ) inside the smoothed quantile regression function. Both sets of parameters need to be tuned to achieve the desired model performance. In the area of deep learning, the integration of quantile regression with neural networks to do uncertainty analysis, which is called quantile regression neural networks, has been studied for years. For example, Taylor (2000) [138] used a quantile regression neural network to estimate the conditional probability distribution of multiperiod financial returns. Quantile regression neural networks have also been used in predicting wind power[66], electricity consumption[67], rainfall extremes[19], and the evaluation of online teaching[113]. In recent years, the adoption of the Huber function to approximate the absolute error function in quantile regression neural networks has gained popularity. Cannon (2010) applied an improved quantile regression neural network to precipitation downscaling [20] and developed an R package called QRNN. Xu et al. (2017) also applied the improved quantile regression neural network to three datasets that have been used before in other papers, and proved that the improved quantile regression neural network had better performance [156]. 68 3.4 EvaluationsofPredictionIntervals Traditional mean prediction results can be estimated using statistical methods, such as root mean square error, mean absolute error, or mean absolute percentage error. The evaluation of the PIs is not as straightforward and there has not been a uniform standard yet. In practice, prediction interval coverage probability (PICP) and prediction interval average width (PIAW) are usually used to quantify PIs [74, 114, 86, 111]. PICP measures the percentage of the target data points that fall in the bounds of the lower and upper limits of the PIs inclusive. The mathematical expression of PICP is represented in equation 3.24 PICP = 1 n n X i=1 c i (3.24) where c i =          1 t i ∈ [y i ,¯y i ] 0 otherwise (3.25) Here,n represents the number of samples.t i is the truei th target value. y i and¯y i are the lower and upper bound of the i t h sample, individually. Large PICP indicates a better model performance. PICP depends on the width of PIs, meaning that a larger PICP usually requires a wider width of PIs. 69 PIAW calculates the average width of PIs. Given that different datasets usually have different sample ranges, PIAW needs to be normalized so that it can be compared across different datasets. The normalized PIAW (PINAW) is given as PINAW = 1 R× n n X j=1 (¯y i − y i ) (3.26) whereR is the range of the observed data. A large width usually indicates higher PICP. However, a very large width is meaningless as it conveys no information about the target values. Thus, a smaller PINAW is always preferred in practice. PICP and PINAW are negatively correlated and they should be used together to co-evaluate the quality of PIs. Between PICP and PINAW, we could control one criteria, and compare the other criteria among different models. For example, we could try to set the PICPs from all models the same and compare PINAWs. The smaller PINAW means a better model performance. However, in real life data, it is hard to control the PICP and PINAW exactly the same. Thus, a new criterion, which combines PICP and PINAW, called the coverage width-based criterion (CWC) was proposed[81] CWC =          PINAW(1+e η (τ − PICP) ) PICP <τ PINAW PICP ≥ τ (3.27) where η = 50 and τ is the desired quantile. CWC is used in practice to assess the quality of PIs across different PI generation methods. All three criteria were looked at in the following experiments to quantify PIs. 70 Table 3.1: Hyperparameter tuning for simulated data. Method learning rate Number of estimators Max depth Huber threshold Quantile GBM 0.05 200 2 – Quantile LightGBM 0.05 200 2 – QXGBoost 0.05 300 3 2 3.5 ExperimentsandResults In this section, we compared PIs generated from three different models, quantile GBM, quantile LightGBM, and QXGBoost, for a toy and a real life traffic noise dataset. For each method, 90% PIs were obtained using two models, one predicting the upper bound of PIs withτ = 0.95 and one for the lower bound withτ = 0.05. For modeling purposes, all datasets were randomly split into 75% and 25% as training and testing datasets, respectively. 3.5.1 ExperimentonSimulatedData The simulation data that we chose was adapted from the scikit-learn library example which demonstrates how quantile regression can be used to create PIs for GBM using the equation 3.28 y = 1.5∗ x∗ sin(x)+ε (3.28) whereε has a normal distribution with mean 0 and a standard deviation that was randomly drawn between 1.5 and 2.5 so that we have heteroscedastic noise for the simulated data. The relationship betweenx andy is not linear. Hyperparameter tuning for the simulated data was shown in table 3.1. All three methods used the same learning rate (0.05). For the extra parameter QXGBoost, the Huber thresholdυ is 71 Table 3.2: Prediction interval results for the toy data. Method Training PICP Testing PICP Testing PINAW Testing CWC Quantile GBM 0.904 0.872 0.733 3.704 Quantile LightGBM 0.901 0.872 0.728 3.682 QXGBoost 0.891 0.892 0.777 1.937 2, within the acceptable range, meaning that the smoothed loss function approximates very close to the original absolute value function. Table 3.2 shows that even though QXGBoost has the smallest training PICP (0.891), it has the largest testing PICP (0.892), meaning that QXGBoost does not have an overfitting problem and can be generalized to other datasets better than quantile LightGBM and quantile GBM. The higher PICP of QXGBoost also comes with a slightly larger PINAW (0.777) which is not very surprising given that higher PICP usually comes with a larger width. Overall, QXGBoost outperformed quantile GBM and LightGBM with the smallest CWC (1.937 VS 3.704 and 3.682). Figure 3.7 shows that all three models have roughly the same PIs whenx < 7. QXGBoost has smaller values for the lower quantile and higher values for the upper quantile when 7 < x < 9 and 9 < x < 10, respectively. However, this is a very simple example with only one independent variablex. For XGBoost, this means that only one variable was used to build all the trees, which leads to a lot of simple numbers added up together. The strong suit of ML methods are their capability to untangle the complex non-linear relationships among the independent variables as illustrated by the real life datasets. 72 Figure 3.7: Comparison of prediction intervals for the toy data using three methods. The dark blue dots are the observations. The red lines are the point predictions of the traffic noise. The two black lines represent the upper and lower bounds of the PIs and the blue areas in between are the PIs. 73 Figure 3.8: Point prediction for traffic noise using GBM, LightGBM, and XGBoost. Blue points represent each observed and predicted sample; solid red lines represent the regression line; and dashed black lines represent the 1:1 correspondence between measured and predicted values. 3.5.2 ExperimentonTrafficNoiseData Traffic noise pollution data consists of 6,647 observations in total, 44 independent variables from different sources, and one dependent variable, the traffic noise to be predicted. More details in terms of how the data were collected were presented in chapter 2. We first run the mean prediction analysis of traffic noise using GBM, LightGBM, and XGBoost. The parameters of each algorithm were tuned by a 5-fold CV random grid search process that included measured average LAeq from all of the observations together. After tuning, each model was trained on 70% of the data and predicted the remaining 30%, the prediction results from which were shown in figure 3.8. XGBoost and GBM have very similar prediction performance with the same R 2 0.97. GBM has a smaller RMSE of 1.81. LightGBM performed slightly worse with a lower R 2 of 0.96 and a higher RMSE of 2.04. The hyperparameter tuning for quantile GBM, LightGBM and QXGBoost was shown in table 3.3. Quantile GBM and LightGBM have the same tree based tuning parameters, and QXGBoost chose a slightly different set of tree parameters with a larger number of trees (300 vs 200) and 74 Table 3.3: Hyperparameter tuning for the traffic noise data. Method Learning rate Number of estimators Max depth Additional Quantile GBM 0.03 200 3 – Quantile LightGBM 0.03 200 3 – QXGBoost 0.05 300 3 0.07 Table 3.4: Prediction interval results for the traffic noise data. Method training PICP Testing PICP Testing PINAW Testing CWC Quantile GBM 0.905 0.890 0.331 4.751 Quantile LightGBM 0.907 0.885 0.320 4.610 QXGBoost 0.902 0.889 0.319 4.580 slower learning rate (0.05 vs 0.03). The additional threshold parameter for the QXGBoostυ equals to 0.07, meaning a good approximation to the real absolute value function. Table 3.4 summarized the training PICP and the testing PICP, PINAW, and CWC from all three models for the traffic noise data. Among the three models, quantile LightGBM has the largest training PICP (0.907) and the smallest testing PICP (0.885), indicating that LightGBM might have an overfitting problem. Even though quantile GBM has the largest testing PICP (0.890), it also has the biggest PI width (0.331). By comparison, QXGBoost has a very close testing PICP (0.889) with a much smaller PINAW (0.319). Overall, QXGBoost has the smallest testing CWC (4.580), followed by quantile LightGBM (4.751) and quantile GBM (4.610). The testing PIs for all three models were shown in figure 3.9, where the x-axis is the measured traffic noise for each observation in the test dataset and y-axis is the PIs of traffic noise in dB represented by the turquoise bars. The first row of figure 3.9 shows that all three models have a wider length of PIs at the lower end of traffic noise and LightGBM tends to over-predict the traffic noise at the lower end than GBM and XGBoost. In terms of the middle level of traffic noise, the PIs of QXGBoost cover most of the extremely high and low point predictions where quantile 75 GBM and LightGBM do not. This is why the PI width of QXGBoost looks wider than quantile GBM and LightGBM in the middle level of noise. One thing to notice for QXGBoost is that it has several very wide length PIs at the high end of traffic noise for some observations, whereas quantile GBM and LightGBM have relatively consistent lengths of PIs, indicating that quantile GBM and LightGBM are more stable than QXGBoost in predicting the high level of traffic noise. Both the first and second row of the figure 3.9 demonstrates that PIs vary in length, with some being much shorter than others. The relatively wider PIs at both ends of the traffic noise are due to the insufficient observations. Figure 3.8 showed that most of the traffic noise values were distributed between 50 and 75 dB and the ones that are below 50 dB or above 75 dB made up only 2.9% and 2.6% of all the observations, respectively. Thus, it is not unexpected that with less training data, models will generate PIs of high uncertainty with wider ranges of PIs. For better visualization, figure 3.10 shows all the traffic noise observations were ordered ac- cording to the length of the corresponding PIs. It can be easily seen that the overall width of PIs of the quantile GBM is wider than that of quantile LightGBM and QXGBoost. QGBoost has a slightly tighter width than quantile LightGBM. All three models performed relatively good at the middle level of traffic noise and covered almost 90% of the observed traffic noise in the testing dataset. Figure 3.11 put the PIs from all three models together to do a direct comparison. Quantile GBM and LightGBM have a wider length of PIs than QXGBoost for most of the observations (around 1300 out of 1649 observations). For the rest of the observations, the PI width of QXGBoost is wider as was reflected at the high index of figure 3.11, indicating that the PI width of QXGBoost varies more than that of quantile GBM and quantile LightGBM. 76 Figure 3.9: PIs for the traffic noise data from all three models. The turquoise lines represent the PIs. The orange points are the point predictions of the traffic noise. The figures on the first row are the PIs for the test set. The figures on the second row are the PIs for 20 randomly selected points. 77 Figure 3.10: Ordered and centered PIs for the traffic noise data from all three models. The orange dots represent the observations that are covered by PIs. The turquoise dots are the observations that are not covered by PIs. The blue areas show the ordered and centered PIs. 3.6 Conclusions In this chapter, we proposed a new method known as QXGBoost that employed quantile regres- sion as the customized objective function for XGBoost to do PI analysis. In order to have an ob- jective function that can be differentiable everywhere, we followed previous studies of replacing the error term in absolute value function with the Huber norm function as a smooth approxima- tion for the quantile regression. To our knowledge, this is the first study that combines quantile regression, the Huber norm function, and XGBoost to do uncertainty analysis for XGBoost. The results from our experiments suggested that QXGBoost can provide better or comparable quality of PIs compared to quantile GBM and LightGBM. 78 Figure 3.11: Ordered and centered PIs from all three models on the same plot. QGBM is quantile GBM, LGBM is quantile LightGBM, and QXGB is quantile XGBoost. 79 The primary goal of this study was to come up with an easy to understand way to implement uncertainty quantification method for XGBoost. Even though the popular uncertainty quantifi- cation methods (such as Bayesian or Delta methods) for neural networks have been studied for years, there might be a learning curve for non-experts to understand these methods. Thus, their integration with XGBoost could also be very challenging or not feasible at all. GBM used the original quantile regression function directly as it does not require second-order approximation for the objective function. LightGBM is similar to XGBoost in terms of the objective optimization method. However, quantile LightGBM involves diving into the source code (C++) and exporting tree leaf indices to the objective function, which could not be done by whoever is not familiar with the LightGBM source code. QXGBoost simply solved the problem by defining an optimized objective function. Even though QXGBoost has one additional parameter to tune, it provides a simple and quick solution for performing uncertainty analysis for one of the most powerful ML methods. The additional threshold hyperparameter τ plays an important role during model fitting. Based on our experiment, τ controls both the PICP and PINAW of the PIs. Small τ (less than 1) usually lead to large PICP and PINAW and largeτ s typically produce small PICP and PINAW, meaning more constraints on the PIs. We prefer large PI coverage with narrower widths. Thus, both the threshold and XGBoost parameters need to be tuned and balanced to achieve better re- sults. However, as is shown in figure 3.5, as τ gets larger (more than 2), the Huber smoothed approximation function will depart further from the quantile regression function, and the poor approximation might lead to biased results. In practice, we want to control the threshold param- eterτ under 2. 80 There are limitations of our method. First, as is shown in figure 3.9, QXGBoost could not give very useful PIs when there are not enough observations, as the PI width is supposed to be very large. This is inevitable given that QXGBoost was built on XGBoost. If XGBoost could not give satisfying point predictions, the corresponding PIs would not be good as well. This also applies for quantile GBM and LightGBM. In figure 3.9, at the extremely low and high ends of the traffic noise, the width of PIs from all three models are uniformly wider than the observations in between, where there are sufficient observations. We generally see overestimation for the low level traffic noise and underestimation for the high level traffic noise. The same also happened to the air pollution remote sensing data. Second, we have not been able to find a way to tune the additional parameters in QXGBoost automatically as we did using the scikit-learn library for other ML methods. The automatic tuning process will be a focus for future work. Third, we usually could not achieve the "hard" coverage as theτ specifies for the proposed QXGBoost method. For example, we have to uniformly pad the quantile intervals by 3% and 1% to get a 90% coverage using QXGBoost for the simulated and traffic noise data, respectively. This limitation is not unique to our method. As is shown in the example in the scikit-garden library, additional padding is also needed for the quantile random forest algorithm to achieve desired quantile coverage. Given these limitations, future efforts should be focued on optimizing the objective function of the XGBoost so that the "hard" coverage can be achieved without additional padding. 81 Chapter4 TheRoleofTrafficNoiseontheAssociationBetweenAir PollutionandChildren’sLungFunctionAfterAccounting forUncertainty 4.1 Introduction The association between exposure to traffic related air pollution and children’s respiratory health has been examined in many cross-sectional and cohort studies [53, 103, 142, 22]. Long-term exposure to air pollution, such as nitrogen oxides (NO, NO 2 , NO x ) [44], ozone (O 3 ) [102], and particulate matter with an aerodynamic diameter less than 2.5µ m (PM 2.5 ) [52] leads to a reduction in lung development in children. Traffic noise, as an environmental stressor, is a possible risk factor for children’s lung func- tion. In Europe, traffic noise ranks second, behind PM 2.5 as the major environmental risk factor for the burden of disease [64]. Although studies have established the adverse health effects of noise on sleep deprivation [134], behavioral health [140], mental health [35], and cardiovascu- lar outcomes [11], the association between noise and respiratory health is just emerging despite 82 the fact that noise shares the same main source as air pollution. In a Europe-wide study, adults with chronically strong annoyance from traffic noise were found to show an increased risk for respiratory health problems [110]. In a German multi-center birth cohort study, the significant negative association between noise and asthma was seen in girls [12]. In the Danish Nurses Cohort study of 24,538 female nurses, Liu et al. [95] found that the hazard ratio for chronic ob- structive pulmonary disease (COPD) was 1.15 (95% CI 1.06, 1.25) per 10 dB for road traffic noise. Furthermore, the association between COPD and NO 2 was attenuated slightly and COPD and PM 2.5 was attenuated to null after adjustment for traffic noise. On the other hand in the Southern California Children’s Health study (CHS), Franklin and Fruin concluded that adjustment for traf- fic noise strengthened the association between NO x and reduced lung function [44], suggesting stress activation from noise could amplify the negative effects of air pollution exposure. Finally, some studies showed no association between noise exposure and lung function [104, 145, 17, 38]. These inconsistencies may reflect inaccurate assessment of exposures. Estimating uncertainty in exposure model predictions is an underutilized but potentially im- portant metric in environmental epidemiological studies. One study showed that uncertainty in exposure estimates increased 50.6% and 38.5% for PM 10 and PM 2.5 , respectively per0.058 ◦ (∼ 6.4 km) distance from the monitoring stations [83]. Failure to account for uncertainty can lead to biased results in exposure-response analyses [154]. For example, after adjusting for exposure un- certainty, risk estimates could change by positive or negative 100% compared to models without adjustment [154, 93, 48]. In a dose response analysis for ultrasound-detected thyroid nodules af- ter exposure to radioactive fallout, researchers found that risk estimates for thyroid nodules from internal irradiation were tripled after accounting for dose uncertainty [87]. The dose-response effect was also found to be doubled in a Nutritional Biomarkers Study of the Women’s Health 83 Initiative after intensive simulation to account for uncertainty [146]. Despite the importance of uncertainty in exposure estimation, few studies have included measurement error or uncertainty in exposure assessments. To the best of our knowledge, no studies so far have examined the role of traffic noise on the association between air pollution and children’s lung function after accounting for its uncertainty. Previous studies suggested that a potential biological pathway for the association between asthma and noise was that the noise-induced stress and/or sleep disturbances were associated with asthma morbidity [120, 158]. Based on a previous study [44], we examined the effect of traffic noise without uncertainty (mean-predicted) on lung function independently in this paper, and traffic noise as a potential confounder to the association between PM 2.5 , traffic NO x , and lung function. Beyond that, we improved our analysis by accounting for the uncertainty estimation in traffic noise, and compared it with the results that did not consider the uncertainty. Children’s lung function measurements were represented by forced expiratory volume in one second (FEV 1 , mL), and forced vital capacity (FVC, mL). 4.2 MaterialandMethods 4.2.1 StudyPopulation The Southern California Children’s Health Study has enrolled more than 11,000 children in a series of five cohorts ever since its inception in the early 1990s. This analysis focuses on the final and most recent cohort, which was initiated in 2002-3 with approximately 3,000 children aged 5-7 years old and examined in 2008, 2010, and 2012 until they were 15–16 years old. These kids resided and went to school in eight communities in the greater Los Angeles, California area: 84 Anaheim, Glendora, Long Beach, Mira Loma, Riverside, Santa Barbara, San Dimas, and Upland. Given that the traffic noise data was only measured and predicted in Long Beach, we focused on the Long Beach community in this study, which has 285 observations across all three years. Long Beach has a wide mixture of different land use and road types including major arterials, lesser arterials, freeways, and a dense network of surface streets, which capture gradients of traffic emissions. Details of the CHS community selection, subject recruitment, and study design have been published previously [115, 115]. 4.2.2 HealthOutcomes From 2007–2012, pulmonary function tests were conducted on each child by trained respiratory staff, measuring FEV 1 and FVC with pressure transducer-based spirometers (ScreenStar Spirome- ters, Morgan Scientific, Haverhill, Massachusetts, USA). A written questionnaire was also admin- istered to obtain information including age, sex, self-identified race, ethnic background, parental education, occurrences of acute respiratory illness, exercise, tobacco-smoke exposure (personal smoking or environmental), and house characteristics (air conditioning, age of house, presence of mildew, pets in the home). Ethnic background in the CHS specifically relates to Hispanic ancestry, identifying Caucasian subjects with Hispanic and non-Hispanic ethnicity [22]. Study protocols were approved by the Institutional Review Board at the University of Southern California (USC), and written informed consent was provided by a parent or legal guardian for all study subjects [149, 52]. 85 4.2.3 EnvironmentalExposures 4.2.3.1 AirPollution Annual 2008, 2010, and 2012 ambient concentrations of freeway and non-freeway NO x were de- rived from the California Line-Source Dispersion Model (CALINE4) [9], which estimates annual average ambient concentration of NO x from local traffic at each study participant’s geocoded residential address for the calendar year before the lung function test. The CALINE4 dispersion model uses information from residential locations, roadway geometry, vehicle traffic volume and emission rate by roadway link, wind speed, wind direction, atmospheric stability, and mixing heights as input variables. These estimated pollutant exposures are regarded as indicators of in- cremental increases in air pollution over background ambient levels due to primary emissions from local vehicular traffic [44] and explains much of the local-scale spatial variation in annual average ambient NO x levels in Southern California [46]. In addition, the ambient concentrations of PM 2.5 from the central monitoring sites in the Long Beach community, which were measured by Federal Reference Method monitors, were also assessed in the models as a comparison to am- bient concentrations of freeway and non-freeway NO x , which might have potential sources of bias from the CALINE4 estimations. 4.2.3.2 TrafficNoise Traffic noise data were included from both mean predictions (Chapter 2) and prediction intervals (Chapter 3). Uncertainty estimations of traffic noise in Long Beach followed the same procedures as mean-predicted traffic noise along the road in chapter 2. The QXGBoost model with best performance from chapter 3 was adopted to predict the traffic noise with uncertainty for each 86 20 m by 20 m grid on the whole surface of Long Beach. Traffic noise uncertainty is represented by the lower and upper bounds of traffic noise associated with each observation generated from QXGBoost. In this study, we used the 90% PIs of traffic noise to do uncertainty analysis and they were linked with CHS participants by latitude and longitude. 4.2.4 StatisticalAnalysis Summary statistics, including the Pearson correlation, were used to characterize the study pop- ulation. Two-sample t tests were used to compare differences of lung function between groups. For our main analysis we fitted mixed effects models with a random effect for participants to consider dependencies between repeatedly measured observations within participants and fixed effects for community and participant-specific covariates. Single pollutant models were fit to as- sess the effects of central-site PM 2.5 , freeway and non-freeway NO x , and mean-predicted noise on measured FVC and FEV 1 . This approach was adopted by previous CHS studies [46, 22, 47]. We also examined noise with and without uncertainty as a potential confounder of the association between central-site PM 2.5 , freeway and non-freeway NO x and lung function. By doing so, we were able to assess how the uncertainty estimation of the traffic noise changed the epidemiolog- ical conclusions about the relationships between air pollution and lung function. To include the uncertainty estimation of traffic noise in the analysis, for each observation, we applied the intensive simulation method without replacement to sample values between the lower and upper bounds of traffic noise. Two sampling strategies, including uniform and truncated Gaussian sampling methods, were employed to show how different simulation methods could affect the epidemiological analysis results. Specifically, for the uniform sampling, we used the 87 runif function in R to generate a predefined number of random variables that were uniformly distributed between the lower and upper bounds of traffic noise. The mixed effects model was fitted iteratively using each set of the generated traffic noise random variables. The coefficient and p-value for each pollutant were extracted in each iteration. This was also done for the Gaussian sampling method, which we used the rnorm function in R to generate the traffic noise variables. The mean value of the Gaussian sampling method for each observation is the mean predicted traffic noise. We used a standard deviation of 4 dB in the Gaussian sampling to allow a maximum of 8 dB of fluctuation for each observation to simulate the traffic noise of different times of the day. Gaussian simulation was confined within the range of the lower and upper bounds of traffic noise, and any simulated value that is beyond this range was assigned to either the lower or upper bound value. Figure 4.1 is an illustration of the two sampling methods with 5000 samples using a lower and upper bound of noise 49.00 and 65.66 dB, respectively, with mean 57.71 dB. Furthermore, different simulation sizes, including 50, 100, 500, 1000, 5000, and 10,000 random noise variables were generated for each sampling method to test the stability of the model. The simulation method has been used in a previous study that incorporated exposure uncertainty estimation in the epidemiological analysis [146]. For each generated traffic noise variable, we assessed its effect on lung function and as a potential confounder of the association between central-site PM 2.5 , freeway and non-freeway NO x , and lung function. All models were adjusted for age, sex, BMI, height, height squared, race/ethnicity, and pres- ence or absence of Hispanic ethnic background with a random intercept for participants. Sta- tistical significance was assessed assuming a 0.05 significance level and a two-sided alternative hypothesis. 88 Figure 4.1: Uniform and Gaussian sampling methods 4.3 Results 4.3.1 SummaryStatistics Summary statistics of the study population, including gender, height, weight, race/ethnicity, and parental education level are shown in table 4.1. There were 115 children with a mean (SD) age of 10.88 (0.61) years who received the lung function test in 2008. About 17% of the participants were lost to follow-up, with 95 children receiving the lung function test in 2010 at a mean age of 13.26 (0.58) years. An additional 21% dropped out in 2012, with 75 kids receiving the lung function test at a mean age of 15.19 (0.58) (table 4.1). The study population consisted of girls and boys with mean spirometric FEV 1 2,382 (415) mL in 2008, 3,094 (518) mL in 2010, and 3,579 (642) mL in 2012, which were a statistically significant difference between each year. FVC were also statistically significantly increased from 2008 with mean 2,707 (503) mL, to 3,527 (644) mL in 2010, and 4,127 (833) mL in 2012. FEV 1 and FVC were significantly higher among boys compared to girls; mean FEV 1 was 3,109 mL among boys and 2,769 mL among girls (t-testp< 0.001), mean FVC was 3,626 89 mL among boys and 3,102 among girls (t-test p < 0.001). The participants who were exposed to second-hand smoke at home had significantly lower lung function with mean FEV 1 2,914 mL (t-testp< 0.05) and FVC 3,335 mL (t-testp< 0.05), respectively. Table 4.1: Characteristics of the study population Characteristic 2008, N = 115 1 2010, N = 95 1 2012, N = 75 1 Sex Boys 59 (51%) 49 (52%) 38 (51%) Girls 56 (49%) 46 (48%) 37 (49%) Age(years) 10.88 (0.61) 13.26 (0.58) 15.19 (0.58) Height(cm) 145 (8) 158 (8) 165 (9) BMI 21.2 (5.1) 22.5 (5.7) 23.8 (5.9) Weight(lbs) 45 (15) 57 (17) 65 (18) Race Asian 14 (12%) 14 (15%) 12 (16%) African American 12 (10%) 5 (5.3%) 7 (9.3%) Caucasian 23 (20%) 22 (23%) 13 (17%) Mixed 14 (12%) 14 (15%) 9 (12%) Other 40 (35%) 30 (32%) 27 (36%) Unknown or missing 12 (10%) 10 (11%) 7 (9.3%) Ethnicity Hispanic 72 (63%) 60 (63%) 47 (63%) Non-Hispanic 34 (30%) 26 (27%) 22 (29%) 90 Unknown or missing 9 (7.8%) 9 (9.5%) 6 (8.0%) ParentsEducation <12 th grade 27 (27%) 22 (28%) 19 (29%) 12 th grade 26 (26%) 16 (20%) 14 (22%) Some college 34 (34%) 31 (39%) 22 (34%) College 8 (8.1%) 6 (7.6%) 8 (12%) Some graduate 4 (4.0%) 4 (5.1%) 2 (3.1%) Exposuretosmoke 4 (3.9%) 13 (14%) 10 (13%) ForcedVitalCapacity(mL) 2,707 (503) 3,527 (644) 4,127 (833) ForcedExpiratoryVolume(mL) 2,382 (415) 3,094 (518) 3,579 (642) FreewayNO x (ppb) 24 (11) 19 (8) 14 (6) Non-freewayNO x (ppb) 10.9 (3.5) 9.1 (3.1) 7.4 (2.4) Noise(dB) 61.7 (3.6) 61.5 (3.6) 62.1 (4.0) LowerlevelofNoise(dB) 53.3 (3.9) 53.3 (4.0) 53.4 (3.8) UpperlevelofNoise(dB) 67.63 (2.97) 67.35 (2.74) 67.59 (2.75) 1 n (%); Mean (SD) Figure 4.2 shows the distributions of the environmental exposures. We observed NO x to be highest for children living closest to major roads. The mean predicted traffic noise varied across different land use, traffic, and meteorological situations in Long Beach with a mean of 61.74 (3.69) dB. The lower bound of traffic noise ranges from 45.14 to 63.40 dB with a mean of 53.33 (3.91) dB, and it shows a similar spatial pattern as the mean predicted traffic noise. It is interesting to see that the high traffic noise of the upper bound were mainly distributed on the south side of Long 91 Figure 4.2: Selected environmental exposures Beach, which is very close to the Long Beach port. This is not unexpected since the Long Beach port is one of the biggest and busiest ports in the nation and idling ships contributed a good deal to the high level noise. The upper bound of traffic noise ranges from 63.17 to 76.55 dB with a mean of 67.53 (2.83) dB. The Pearson correlations between freeway NO x , non-freeway NO x , mean-predicted noise, and the central site PM 2.5 are shown in table 4.2. Over the period, the mean predicted noise was positively correlated with freeway NO x (r = 0.04) and also significantly correlated with non- freeway NO x (r = 0.37,p< 0.001). The correlation between freeway NO x , non-freeway NO x and central site PM 2.5 were also positive and statistically significant, with r = 0.40 (p < 0.001) and r = 0.42 (p< 0.001), respectively. Freeway NO x and non-freeway NO x were not correlated with each other (r = 0.40). To avoid highly correlated variables, none of the pollutants were included in the same model except when examining noise as a potential confounder. 92 Table 4.2: Pearson correlation coefficients for environmental risk factors FreewayNO x (ppb) Non-FreewayNO x (ppb) Noise(dB) PM 2.5 (µg/m 3 ) FreewayNO x (ppb) 1.00 0.03 0.04 0.40 Non-FreewayNO x (ppb) 1.00 0.37 0.42 Noise(dB) 1.00 -0.04 PM 2.5 (µg/m 3 ) 1.00 93 4.3.2 MainAnalysesWithoutUncertainty Table 4.3 shows the results of FEV 1 from the models with and without adjusting for traffic noise. In the unadjusted models, a unit increase in PM 2.5 showed a non-significant -95.42 mL decrease (95% CI -197.98, 7.14) in FEV 1 . The FEV 1 decrease associated with a unit increase in freeway NO x , non-freeway NO x , and traffic noise was -0.50 mL (95% CI -5.39, 4.39), -6.08 mL (95% CI -21.82, 9.65), and -8.44 mL (95% CI -20.81, 3.93), respectively. After adjusting for the mean-predicted traffic noise, the association between a unit increase of PM 2.5 and FEV 1 was increased to -97.75 mL (95% CI -199.50, 3.99), and it was decreased to -0.32 mL (95% CI -5.20, 4.55) and -2.48 mL (95% CI -19.40, 14.45) for freeway NO x and non-freeway NO x . Similar results were found for FVC (Table 4.3). The effect estimate without adjustment for noise indicated a non-significant -119.53 mL decrease (95% CI -241.63, 2.57) in FVC per unit in- crease in PM 2.5 . The estimates for freeway NO x , non-freeway NO x , and traffic noise was -1.04 mL (95% CI -6.78, 4.71), -5.04 mL (95% CI -23.53, 13.45), and -7.39 mL (95% CI -21.90, 7.11), respectively. After adjusting for the mean-predicted traffic noise, the association between a unit increase of PM 2.5 and FVC was increased to -121.55 mL (95% CI -243.25, 0.15), and it was decreased to -0.85 mL (95% CI -6.60, 4.89) and -1.87 mL (95% CI -21.76, 18.03) for freeway NO x and non-freeway NO x . The results indicated that traffic noise did not confound the relationship between PM 2.5 and lung function, but it did confound the relationship between freeway NO x and FEV 1 and FVC, by 36.0% and 18.3%, and non-freeway NO x , by 59.2% and 62.9%, respectively. 94 Table 4.3: Estimated linear associations between FEV 1 and environmental factors from unadjusted and adjusted models Notadjusted Adjusted Exposure Estimate 95%CI pvalue Estimate 95%CI pvalue PM 2.5 -95.42 (-197.98, 7.14) 0.07 -97.75 (-199.50, 3.99) 0.06 FreewayNO x -0.50 (-5.39, 4.39) 0.84 -0.32 (-5.20, 4.55) 0.90 Non-FreewayNO x -6.08 (-21.82, 9.65) 0.45 -2.48 (-19.40, 14.45) 0.77 Noise -8.44 (-20.81, 3.93) 0.18 - - - Table 4.4: Estimated linear associations between FVC and environmental factors from unadjusted and adjusted models NotAdjusted Adjusted Exposure Effectestimate 95%CI pvalue Effectestimate 95%CI pvalue PM 2.5 -119.53 (241.63, 2.57) 0.05 -121.55 (-243.25, 0.15) 0.05 FreewayNO x -1.04 (-6.78, 4.71) 0.72 -0.85 (-6.60, 4.89) 0.77 Non-FreewayNO x -5.04 (-23.53, 13.45) 0.59 -1.87 (-21.76, 18.03) 0.85 Noise -7.39 (-21.90, 7.11) 0.32 - - - 95 Table 4.5: The mean and SD of the traffic noise coefficients from single exposure models based on different numbers of simulations Uniformsampling Gaussiansampling Simulationsize FEV 1 FVC FEV 1 FVC 50 -6.36 (3.97) -6.05 (4.79) -5.84 (4.13) -6.04 (4.82) 100 -6.28 (3.72) -6.15 (4.56) -5.61 (3.91) -5.41 (4.57) 500 -5.82 (3.87) -5.51 (4.77) -5.66 (3.88) -5.58 (4.49) 1,000 -5.70 (3.90) -5.37 (4.80) -5.52 (3.76) -5.43 (4.46) 5,000 -5.60 (4.02) -5.31 (4.87) -5.44 (3.92) -5.36 (4.71) 10,000 -5.55 (4.04) -5.26 (4.89) -5.41 (3.92) -5.33 (4.73) 4.3.3 MainAnalysesWithUncertainty Table 4.5 shows the results of the association between FEV 1 and FVC with traffic noise after ac- counting for uncertainty. The association was examined using both uniform and Gaussian sam- pling methods with different simulation sizes. In general, as the simulation size increases, the average coefficient of noise becomes more stable. The coefficients vary a lot when the simulation size is below 1,000. The coefficient difference was smaller between 5,000 and 10,000 simulations than between 1,000 and 5,000, indicating that 5,000 simulations is reliable enough to generate robust epidemiological results. Thus, for the other pollutant analysis adjusted for traffic noise uncertainty, we used the maximum simulation size of 5,000. Compared to table 4.3 and 4.4 where the coefficients of the mean-predicted traffic noise were -8.44 and -7.39 for FEV 1 and FVC, respec- tively, the average coefficients were smaller for both FEV 1 and FVC after accounting for uncer- tainty of noise. The coefficients were 33.6% and 28.1% smaller for FEV 1 and FVC using uniform sampling method and 35.5% and 27.5% smaller using Gaussian sampling method when compared to the average coefficients from 5,000 simulations. The results from both sampling methods were very close. 96 In the mixed effects models of pollutants adjusted for traffic noise with uncertainty, we did not see a big difference of results between the uniform and Gaussian sampling methods. However, the results from the Gaussian sampling are closer to the ones from traffic noise without uncertainty. The average coefficient of each pollutant varies less among different simulation sizes compared to the coefficients from table 4.5 when only traffic noise with uncertainty were included in the models. Using the simulation size of 5,000 as standard, after accounting for the uncertainty of traffic noise, the average coefficient of PM 2.5 dropped from 97.75 when adjusted for traffic noise without uncertainty to 96.24 from uniform sampling and 96.56 from Gaussian sampling for FEV 1 and it dropped from 121.55 to 120.29 and 120.61 for FVC. In figure 4.3 and 4.4 where the second rows show the confidence interval (CI) distribution of PM 2.5 , the lower bound of CI has 406 and 320 out of 5,000 that are less than 0 for FEV 1 and 1,184 and 1,205 for FVC, respectively, indicating statistically significant associations of PM 2.5 with the corresponding outcome using different sam- pling methods. Thus, false exposure-outcome conclusions could be reached if the mean-predicted traffic noise fell into these categories. The confounding effect of traffic noise to the freeway and non-freeway NO x and lung function were much more diminished after accounting for the uncertainty of traffic noise. In the uniform sampling of traffic noise, the effect of freeway NO x on FEV 1 did not change at all after adjusting for traffic noise with uncertainty, and still remains -0.50. In the Gaussian sampling, traffic noise only accounted for 14% of the effect between freeway NO x and FEV 1 , smaller than 36.0% when adjusting for the mean-predicted traffic noise. This is the same for freeway NO x and FVC, traf- fic noise did not change the coefficient of freeway NO x in the uniform sampling, and changed 6.7% in the Gaussian sampling, smaller than 18.3% when adjusting for the mean-predicted traffic 97 Table 4.6: The mean and SD of air pollution coefficients from single exposure models based on different numbers of simulations Uniformsampling Gaussiansampling Exposures Simulation size FEV 1 FVC FEV 1 FVC PM 2.5 50 -95.31 (5.15) -119.05 (4.52) -96.79 (3.84) -120.56 (3.99) 100 -96.26 (5.32) -120.16 (5.31) -96.32 (3.77) -120.19 (3.79) 500 -96.07 (4.33) -120.10 (4.28) -96.38 (4.03) -120.37 (4.22) 1,000 -96.33 (4.34) -120.32 (4.33) -96.42 (3.91) -120.40 (3.99) 5,000 -96.24 (4.48) -120.29 (4.59) -96.56 (3.79) -120.61 (3.96) FreewayNO x 50 -0.48 (0.21) -1.02 (0.21) -0.42 (0.18) -0.95 (0.20) 100 -0.50 (0.20) -1.04 (0.20) -0.43 (0.18) -0.97 (0.18) 500 -0.51 (0.19) -1.03 (0.19) -0.42 (0.17) -0.96 (0.18) 1,000 -0.50 (0.20) -1.03 (0.20) -0.42 (0.17) -0.96 (0.18) 5,000 -0.50 (0.20) -1.03 (0.20) -0.43 (0.16) -0.97 (0.17) Non-freewayNO x 50 -3.76 (1.93) -2.84 (2.04) -4.15 (1.63) -3.06 (1.81) 100 -3.83 (1.77) -2.84 (1.95) -4.27 (1.57) -3.33 (1.71) 500 -4.08 (1.72) -3.18 (1.97) -4.25 (1.57) -3.22 (1.73) 1,000 -4.15 (1.70) -3.24 (1.93) -4.32 (1.50) -3.29 (1.71) 5,000 -4.17 (1.75) -3.24 (1.96) -4.36 (1.60) -3.32 (1.82) noise. This result indicates that without uncertainty, traffic noise was a confounder between free- way NO x and lung function. However, this confounding effect disappeared after accounting for the uncertainty of traffic noise. For non-freeway NO x , traffic noise confounded 31.4% (uniform sampling) and 28.3% (Gaussian sampling) for its relationship between FEV 1 , and 35.7% (uniform sampling) and 34.1% (Gaussian sampling) for FVC, much smaller than 59.2% and 62.9% when only adjusting for the mean-predicted traffic noise. The CIs of the corresponding exposures in figure 4.5, 4.6, 4.7, and 4.8 have wider ranges than the CIs adjusting for traffic noise without uncertainty, represented by the dashed black line in each figure, indicating higher uncertainty of the effect of exposures after accounting for traffic noise with uncertainty. 98 Figure 4.3: The coefficients and confidence interval distributions of PM 2.5 for FEV 1 after account- ing for traffic noise with uncertainty. 99 Figure 4.4: The coefficients and confidence interval distributions of PM 2.5 for FVC after accounting for traffic noise with uncertainty. 100 Figure 4.5: The coefficients and confidence interval distributions of freeway NO x for FEV 1 after accounting for traffic noise with uncertainty. 101 Figure 4.6: The coefficients and confidence interval distributions of freeway NO x for FVC after accounting for traffic noise with uncertainty. 102 Figure 4.7: The coefficients and confidence interval distributions of non-freeway NO x for FEV 1 after accounting for traffic noise with uncertainty. 103 Figure 4.8: The coefficients and confidence interval distributions of non-freeway NO x for FVC after accounting for traffic noise with uncertainty. 104 4.4 DiscussionandConclusions In this study, we linked central site measured PM 2.5 , traffic related air pollution, and traffic noise to a cohort of children in Southern California with measured health data. By doing so, we were able to conduct epidemiological assessments of their associations with children’s lung function, including the marginal and joint effects of PM 2.5 , freeway and non-freeway NO x , and traffic noise. In particular, we incorporated the uncertainty estimate of traffic noise into the exposure-response analysis. The traffic noise uncertainty estimation was calculated from our proposed QXGBoost method, from which we got the upper and lower bounds of traffic noise based on the 90% quantile prediction intervals. This specific form of uncertainty allows us to explore the effect of different sampling strategies and sample sizes on exposure-response analysis. In the main analysis without traffic noise uncertainty, we observed that traffic related air pollution including freeway, non-freeway NO x , and traffic noise were not statistically signif- icantly related with lung function, which were consistent with previous CHS studies using a larger dataset and including all eight study communities [44]. Even though we did not find a statistically significant relationship ( p < 0.05) between central site PM 2.5 with lung function, it is marginally significantly related with FEV 1 and FVC (p < 0.1). In a previous CHS study that examined the cross-sectional effect of central site PM 2.5 on lung function that used the data in year 2008, Urman et al. [142] found that central site PM 2.5 was significantly associated with both FEV 1 and FVC. In the models adjusted for the mean-predicted traffic noise, we found that the inclusion of traffic noise enhanced the negative association between central site PM 2.5 and both FEV 1 and FVC. However, it diminished the negative association between both freeway and non- freeway NO x and FEV 1 and FVC. In a similar CHS study that also looked at the marginal and joint 105 effects of traffic air pollution and noise, Franklin and Scott [44] found that the inclusion of noise amplified the strength of the negative association between freeway NO x and both FVC and FEV 1 . The discrepancies between Franklin and Scott’s study and our study can be explained by several potential reasons. First, Franklin and Scott’s study used all eight study communities in CHS and it is a cross-sectional study, which focused only on year 2012. Our study, on the other hand is a longitudinal study which used data from years 2008, 2010, and 2012, but only focused on the Long Beach community with less observations in the analysis. Second, the traffic noise data from Franklin and Scott’s study was extracted from the Traffic Noise Model (TNM) developed by the U.S. Federal Highway Administration (FHWA). In one of our studies, we found that TNM over- estimated the residential area traffic noise by over 10 dB [40]. So the traffic noise might not be accurate enough to capture the true relationships in the exposure-response analysis. Third, the noise estimation in Franklin and Scott’s study did not account for uncertainty. Based on the main analysis results accounting for uncertainty, we saw that different sets of traffic noise variables lead to different conclusions, and the true causal effect relationships could not be defined by any single set of variables. Nevertheless, when the uncertainty of traffic noise was not considered, we concluded that noise adds a negative effect on the association between PM 2.5 and lung function, but acts as a positive confounder on the association between freeway and non-freeway NO x and lung function. Given the infinitely possible values between the lower and upper bounds of traffic noise for each participant, it is important to understand the necessary numbers of simulations that could lead to stable results. In our study, we saw that in general, as the simulation number increases, the coefficient estimation becomes more stable as is indicated by the smaller variation of stan- dard deviation. Previous studies that employed simulated data to explore the effect of exposure 106 uncertainty usually use 1,000 simulations [151, 127]. In our analyses of lung function and traffic noise with uncertainty, we saw that the average coefficient of traffic noise fluctuated less from 5,000 to 10,000 than from 1,000 to 5,000 simulations, indicating that more than 5,000 simulations could generate more robust results. However, adjusting for the traffic noise with uncertainty in the models, we found that even a smaller simulation size of around 500 could generate relatively stable results. One possible explanation is that since we saw no significant relationship between each of the pollutants with lung function in the unadjusted models, it is unlikely that the variation of traffic noise could greatly change the coefficient of the pollutant. Thus, the necessary simula- tion numbers could vary from study to study, depending on different data and models. However, it should be noted that as the numbers of simulations go up, it could become computationally intensive even for a very small sample size, like 285 in our study. A balance between the number of simulations and robust results should be considered. Studies have shown that the exposure concentrations that did not account for uncertainty would result in underestimating true health effects [121, 127]. A limitation of many studies that have been performed so far is the exposure assessment. In our study, we proved that failure to account for exposure uncertainty in the epidemiological analysis could exaggerate the true causal effect between exposures and health outcomes. For example, in the mixed effects model that adjusted for the traffic noise without uncertainty, we saw traffic noise confounded 36.0% and 18.3% between the relationship of freeway NO x and FEV 1 and FVC, and 59.2% and 62.9% of non- freeway NO x , respectively. However, after accounting for the uncertainty, traffic noise was no longer a confounder in the association between freeway NO x and lung function (the coefficients of FEV 1 and FVC changed less than 10%). The confounding effect of traffic noise was attenuated to 107 28.3% (uniform sampling) and 34.1% (Gaussian sampling) compared to the 62.9% using the mean- predicted traffic noise. In the models adjusted for central site PM 2.5 , we saw that the results were relatively robust to the uncertainty of traffic noise, because the coefficients and the relationships between PM 2.5 and lung function did not change regardless of the traffic noise. This is mainly due to the stronger effect of PM 2.5 on FEV 1 and FVC than either freeway or non-freeway NO x . Their relationships could hardly be altered by the non-significant traffic noise variable, even with uncertainty. Some studies concluded that epidemiological findings were relatively robust to the exposure error when the bias was small [151]. Between the uniform and Gaussian sampling methods, it is not unexpected that the results of the Gaussian sampling method are closer to the results using traffic noise without uncertainty given that the sampled values of the Gaussian method are more clustered around the mean. Thus, the Gaussian sampling method is a preferable choice if we assume that the mean predicted traffic noise is the best prediction of the true traffic noise. In some of the models in table 4.6, we did not see a big difference in terms of the coefficient estimation between the two sampling methods. There could be two possible explanations. First, the sample size in our epidemiological analyses is too small as we only have 285 available observations. We would expect to see a bigger difference between the uniform and Gaussian sampling methods if we have a larger sample size. Second, the uncertainty intervals of traffic noise are not very large, mostly between 10 to 16 dB, which might result in a similar sampling result for uniform and Gaussian methods with a standard deviation of 4 dB. There are some limitations of our study. First, the annual estimation of traffic noise and its uncertainty were predicted only at one point in the year 2019, but the lung function measurements were conducted over three years in 2008, 2010, and 2012. Therefore, we must assume that the 108 exposures are representative of the time of diagnosis. However, the mismatch of the time between exposure and health outcomes might be possible. Second, the analyses were constrained by the small sample size. As our traffic noise measurement and prediction were only in Long Beach, the epidemiological assessment of lung function was limited to Long Beach too. Future studies could focus on collecting more traffic noise data in more communities in the CHS so that the conclusions in this paper could be tested. 109 Chapter5 Conclusions In chapter 2, we adopted a mobile data collection method to measure traffic noise and used ML techniques, including linear regression, random forest, XGBoost, and a neural network to predict traffic noise in Long Beach. Input variables to the models included traffic metrics, road network features, meteorological conditions, and different land use types. Among all ML models, XGBoost had the best results in validation tests in both 5-fold and LORO CV. Finally, with the optimal XG- Boost model we mapped traffic noise along roads at a fine 20 m spatial resolution in Long Beach. We show that a novel, on-foot mobile noise measurement method coupled with ML approaches enables highly accurate predictions of small-scale spatial patterns in traffic-related noise over a mixed-use urban area. In chapter 3, taking advantage of the customizable property of XGBoost, we proposed a new uncertainty quantification method QXGBoost, which combines XGBoost and quantile regression to generate PIs. Given that the objective function in XGBoost was optimized using the second- order approximation, we included the Huber norm in the quantile regression model to construct a differentiable approximation to the absolute value function of quantile regression. This key step 110 allows the existence of both the first and second order derivatives of the proposed objective func- tion and the gradient-based optimization algorithm in XGBoost to make probabilistic predictions more efficiently. QXGBoost was applied to a simulated dataset and the traffic noise data gener- ated in chapter 2. The results showed that QXGBoost had comparable or better performance in both datasets compared to quantile GBM and LightGBM. With QXGBoost, we were also able to generate 90% PIs of traffic noise for each 20m× 20m grid in Long Beach. In chapter 4, we linked the generated traffic noise with and without uncertainty to each child in the CHS by latitude and longitude to assess the effect of traffic related pollutants on lung func- tion. We conducted two types of analysis. First, we examined the associations between traffic noise, PM 2.5 , freeway, and non-freeway NO x with FEV 1 and FVC. Then, traffic noise was evalu- ated as a potential confounder on the association between PM 2.5 , freeway, and non-freeway NO x with FEV 1 and FVC. Both analyses were done using mixed effects models. Traffic noise without and with uncertainty from chapter 2 and 3, respectively were included in each model to do a comparison. Two sampling strategies, uniform and Gaussian methods with varying simulation sizes, were considered to represent traffic noise with uncertainty. Our study showed that without considering the exposure uncertainty, the true effect of exposures might be exaggerated. Between the two sampling methods, the results from the Gaussian sampling method was closer to models without accounting for uncertainty. Last but not least, we tried to answer the question "how many simulations are good enough to get stable results?" Our study shows that there is not a single number that fits all problems. It depends on the study. 111 5.1 Strengths Previous noise prediction studies have typically relied on fixed-site monitoring to measure traffic noise. As the first study of its kind, the results from our study show the potential of combining spatially-resolved walking noise measurements with ML methods. In our other study that eval- uates different traffic noise prediction methods over a large urban area, it was shown that our mobile data collection method together with XGBoost gave the best overall model performance across varying road types, especially on secondary, tertiary, and residential roads. One important strength of the QXGBoost model is that it is easy to understand and implement. Developing a customized objective function using a modified quantile regression function means that we do not need to rewrite the original source code of XGBoost (C++) to achieve the same goal. Quantile regression has been applied to GBM, random forest, and neural networks to get PI estimation for these advanced ML methods. However, this is the first time it’s been applied to XGBoost. QXGBoost is also fast to compute thanks to the high efficiency of XGBoost. Given the PIs for traffic noise generated by QXGBoost, we were able to evaluate how uncertainty in expo- sures affect the model accuracy in exposure-response analysis. To the best of our knowledge, this is one of the first studies that accounted for uncertainty of exposure in a real life epidemiological dataset rather than a simulated one. 5.2 Limitations Although the mobile noise measurements together with XGBoost were proven to have the best performance, walking into neighborhoods with noise measurement instruments is still labor in- tensive, especially for large areas like Southern California. The reliable instruments that were 112 used to collect the traffic noise data were very expensive, which can be financially challenging to be deployed at multiple locations simultaneously on a tight budget. XGBoost also required the extraction of a large set of predictor variables from various sources, which may result in incom- plete data. For example, different types of land use data were proven to be important in predicting traffic noise. However, the building information for most areas from OSM are far from complete. Despite the fact that QXGBoost is easy to implement, it is sensitive to the parameter tun- ing, especially for the additional parameter that was introduced from the Huber norm function. Internally, XGBoost uses the Hessian diagonal to rescale the gradient, the Hessian matrix from the modified quantile regression function makes XGBoost a bit more sensitive to step size. The task of parameter auto-tuning remains difficult given that the evaluation metric for PIs is still not available. With that being said, it requires several rounds of trial and error and a better un- derstanding of how the proposed objective function works to get better model performance with desired probability coverage and small prediction interval width. QXGBoost sometimes strug- gles to achieve the desired quantiles defined by models. Additional paddings for quantiles might be needed. This issue is not unique to QXGBoost. Quantile random forest sometimes requires additional padding too. Our epidemiological analyses that account for traffic noise uncertainty was constrained by the limited sample size. The conclusions about comparisons between different sampling methods and necessary simulation numbers might be different with a larger sample size. 113 5.3 FutureDevelopment As accurate exposure estimation in environmental epidemiological studies is crucial for health risk assessment, our study has contributed to the ongoing effort of including exposure uncertainty in the epidemiological analysis as well as developing a new method to estimate exposure uncer- tainty. QXGBoost produced comparable results to quantile GBM and LightGBM when applied to simulated and real life traffic noise data. There is, however, still great room for improvement in terms of optimizing parameters and achieving parameter auto-tuning, which requires defining an evaluation metric for the model to assess the quality of produced PIs. Efforts should also be made to improve the modified quantile regression function to achieve the desired quantiles with- out additional padding, which might not be possible by simply defining the objective function for XGBoost like we did in this study. However, other methods might be worth exploring. For ex- ample, LightGBM, which also relies on second-order approximation, was successfully combined with quantile regression and achieved user-defined quantiles without additional padding. Their success relies on rewriting the source code of LightGBM. In this study, I was not able to incorpo- rate quantile regression into XGBoost like it was in LightGBM as it involves exporting tree leaf indices to the objective function. Future studies should focus on achieving this goal as it would be expected to improve the model performance. This is a potentially interesting area of research. Future studies could focus on collecting more traffic noise data in more communities in the CHS so that the conclusions in chapter 4 could be tested. Our results were robust as we simu- lated the traffic noise data and ran the mixed effects models 5,000 times. However, it would be interesting to see how our exposure-response results would change if our methods were applied to a larger sample size. 114 Bibliography [1] AADT Traffic Volumes | Caltrans .url: https://imsc.usc.edu/adms/index.html. [2] AADT Traffic Volumes | Caltrans .url: https://dot.ca.gov/programs/traffic-operations/census/traffic-volumes. [3] Moloud Abdar, Farhad Pourpanah, Sadiq Hussain, Dana Rezazadegan, Li Liu, Mohammad Ghavamzadeh, Paul Fieguth, Xiaochun Cao, Abbas Khosravi, U Rajendra Acharya, et al. “A review of uncertainty quantification in deep learning: Techniques, applications and challenges”. In: Information Fusion (2021). [4] Inmaculada Aguilera, Maria Foraster, Xavier Basagaña, Elisabetta Corradi, Alexandre Deltell, Xavier Morelli, Harish C Phuleria, Martina S Ragettli, Marcela Rivera, Alexandre Thomasson, et al. “Application of land use regression modelling to assess the spatial distribution of road traffic noise in three European cities”. In: Journal of exposure science & environmental epidemiology 25.1 (2015), pp. 97–105. [5] Happy Aprillia, Hong-Tzer Yang, and Chao-Ming Huang. “Statistical load forecasting using optimal quantile regression random forest and risk assessment index”. In: IEEE Transactions on Smart Grid 12.2 (2020), pp. 1467–1480. [6] Abnash Bassi, Anika Shenoy, Arjun Sharma, Hanna Sigurdson, Connor Glossop, and Jonathan H Chan. “Building Energy Consumption Forecasting: A Comparison of Gradient Boosting Models”. In: The 12th International Conference on Advances in Information Technology. 2021, pp. 1–9. [7] Colin Bellinger, Mohomed Shazan Mohomed Jabbar, Osmar Zaıäne, and Alvaro Osornio-Vargas. “A systematic review of data mining and machine learning for air pollution epidemiology”. In: BMC public health 17.1 (2017), pp. 1–19. [8] Gareth Bennett, Eoin A King, Jan Curn, Vinny Cahill, F Bustamante, and Henry J Rice. “Environmental noise mapping using measurements in transit”. In: Proceedings of ISMA. 2010, pp. 1795–1810. 115 [9] Paul E Benson. “A review of the development and application of the CALINE3 and 4 models”. In:AtmosphericEnvironment.PartB.UrbanAtmosphere 26.3 (1992), pp. 379–390. [10] Candice Bentéjac, Anna Csörgő, and Gonzalo Martıńez-Muñoz. “A comparative analysis of gradient boosting algorithms”. In: Artificial Intelligence Review 54.3 (2021), pp. 1937–1967. [11] Natalya Bilenko, Lenie van Rossem, Bert Brunekreef, Rob Beelen, Marloes Eeftens, Gerard Hoek, Danny Houthuijs, Johan C De Jongste, Elise van Kempen, Gerard H Koppelman, et al. “Traffic-related air pollution and noise and children’s blood pressure: results from the PIAMA birth cohort study”. In: European journal of preventive cardiology 22.1 (2015), pp. 4–12. [12] Angelina Bockelbrink, Stefan N Willich, Irina Dirzus, Andreas Reich, Susanne Lau, Ulrich Wahn, and Thomas Keil. “Environmental noise and asthma in children: sex-specific differences”. In: Journal of Asthma 45.9 (2008), pp. 770–773. [13] Leo Breiman. “Random forests”. In: Machine learning 45.1 (2001), pp. 5–32. [14] Bert Brunekreef and Stephen T Holgate. “Air pollution and health”. In: The lancet 360.9341 (2002), pp. 1233–1242. [15] Ming Cai, Ziqin Lan, Zhiwei Zhang, and Haibo Wang. “Evaluation of road traffic noise exposure based on high-resolution population distribution and grid-level noise data”. In: Building and Environment 147 (2019), pp. 211–220. [16] Ming Cai, Jingfang Zou, Jiemin Xie, and Xialin Ma. “Road traffic noise mapping in Guangzhou using GIS and GPS”. In: Applied Acoustics 87 (2015), pp. 94–102. [17] Yutong Cai, Wilma L Zijlema, Dany Doiron, Marta Blangiardo, Paul R Burton, Isabel Fortier, Amadou Gaye, John Gulliver, Kees De Hoogh, Kristian Hveem, et al. “Ambient air pollution, traffic noise and adult asthma prevalence: a BioSHaRE approach”. In: European Respiratory Journal 49.1 (2017). [18] Arnaud Can, Luc Dekoninck, and Dick Botteldooren. “Measurement network for urban noise assessment: Comparison of mobile measurements and spatial interpolation approaches”. In: Applied acoustics 83 (2014), pp. 32–39. [19] Alex J Cannon. “Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network, with application to rainfall extremes”. In: Stochastic environmental research and risk assessment 32.11 (2018), pp. 3207–3225. [20] Alex J Cannon. “Quantile regression neural networks: Implementation in R and application to precipitation downscaling”. In: Computers & geosciences 37.9 (2011), pp. 1277–1284. 116 [21] Ta-Yuan Chang, Chih-Hsiang Liang, Chang-Fu Wu, and Li-Te Chang. “Application of land-use regression models to estimate sound pressure levels and frequency components of road traffic noise in Taichung, Taiwan”. In: Environment international 131 (2019), p. 104959. [22] Khang Chau, Meredith Franklin, and W James Gauderman. “Satellite-derived PM2. 5 composition and its differential effect on children’s lung function”. In: Remote Sensing 12.6 (2020), p. 1028. [23] Colin Chen. “A finite smoothing algorithm for quantile regression”. In: Journal of Computational and Graphical Statistics 16.1 (2007), pp. 136–164. [24] Tianqi Chen and Carlos Guestrin. “Xgboost: A scalable tree boosting system”. In: Proceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining. 2016, pp. 785–794. [25] Tianqi Chen, Tong He, Michael Benesty, Vadim Khotilovich, Yuan Tang, Hyunsu Cho, et al. “Xgboost: extreme gradient boosting”. In:Rpackageversion0.4-2 1.4 (2015), pp. 1–4. [26] Xing Chen, Li Huang, Di Xie, and Qi Zhao. “EGBMMDA: extreme gradient boosting machine for MiRNA-disease association prediction”. In: Cell death & disease 9.1 (2018), pp. 1–16. [27] Zhao-Yue Chen, Tian-Hao Zhang, Rong Zhang, Zhong-Min Zhu, Jun Yang, Ping-Yan Chen, Chun-Quan Ou, and Yuming Guo. “Extreme gradient boosting model to estimate PM2. 5 concentrations with missing-filled satellite data in China”. In: Atmospheric Environment 202 (2019), pp. 180–189. [28] Bowen Cheng, Yuxia Ma, Fengliu Feng, Yifan Zhang, Jiahui Shen, Hang Wang, Yongtao Guo, and Yifan Cheng. “Influence of weather and air pollution on concentration change of PM2. 5 using a generalized additive model and gradient boosting machine”. In: Atmospheric Environment 255 (2021), p. 118437. [29] Hugh A Chipman, Edward I George, and Robert E McCulloch. “BART: Bayesian additive regression trees”. In: The Annals of Applied Statistics 4.1 (2010), pp. 266–298. [30] Yinghao Chu, Mengying Li, Hugo TC Pedro, and Carlos FM Coimbra. “Real-time prediction intervals for intra-hour DNI forecasts”. In: Renewable Energy 83 (2015), pp. 234–244. [31] Charlotte Clark, Hind Sbihi, Lillian Tamburic, Michael Brauer, Lawrence D Frank, and Hugh W Davies. “Association of long-term exposure to transportation noise and traffic-related air pollution with the incidence of diabetes: a prospective cohort study”. In: Environmental health perspectives 125.8 (2017), p. 087025. 117 [32] John W Coulston, Dennis M Jacobs, Chris R King, and Ivey C Elmore. “The influence of multi-season imagery on models of canopy cover”. In: Photogrammetric Engineering & Remote Sensing 79.5 (2013), pp. 469–477. [33] DarkSky Weather.url: https://darksky.net/forecast/40.7127,-74.0059/us12/en. [34] DMV Vehicle Fuel Type Count by Zip Code.url: https://data.ca.gov/dataset/vehicle-fuel-type-count-by-zip-code. [35] Stefanie Dreger, Nicole Meyer, Hermann Fromme, Gabriele Bolte, et al. “Environmental noise and incident mental health problems: A prospective cohort study among school children in Germany”. In: Environmental research 143 (2015), pp. 49–54. [36] J Dutta, Yong Woon Kim, and Dalia Dominic. “Comparison of Gradient Boosting and Extreme Boosting Ensemble Methods for Webpage Classification”. In: 2020 Fifth International Conference on Research in Computational Intelligence and Communication Networks (ICRCICN). IEEE. 2020, pp. 77–82. [37] Rachid Errouissi, Julian Cardenas-Barrera, Julian Meng, Eduardo Castillo-Guerra, Xun Gong, and Liuchen Chang. “Bootstrap prediction interval estimation for wind speed forecasting”. In: 2015 IEEE Energy Conversion Congress and Exposition (ECCE). IEEE. 2015, pp. 1919–1924. [38] Ikenna C Eze, Maria Foraster, Emmanuel Schaffner, Danielle Vienneau, Harris Héritier, Reto Pieren, Laurie Thiesse, Franziska Rudzik, Thomas Rothe, Marco Pons, et al. “Transportation noise exposure, noise annoyance and respiratory health in adults: A repeated-measures study”. In: Environment international 121 (2018), pp. 741–750. [39] Masoud Fallah-Shorshani, Laura Minet, Rick Liu, Céline Plante, Sophie Goudreau, Tor Oiamo, Audrey Smargiassi, Scott Weichenthal, and Marianne Hatzopoulou. “Capturing the spatial variability of noise levels based on a short-term monitoring campaign and comparing noise surfaces against personal exposures collected through a panel study”. In: Environmental research 167 (2018), pp. 662–672. [40] Masoud Fallah-Shorshani, Xiaozhe Yin, Rob McConnell, Meredith Franklin, et al. “Estimating traffic noise over a large urban area: an evaluation of methods”. In: Meredith, Estimating Traffic Noise Over a Large Urban Area: An Evaluation of Methods (). [41] Junliang Fan, Xin Ma, Lifeng Wu, Fucang Zhang, Xiang Yu, and Wenzhi Zeng. “Light Gradient Boosting Machine: An efficient soft computing model for estimating daily reference evapotranspiration with local and external meteorological data”. In: Agricultural Water Management 225 (2019), p. 105758. 118 [42] Junliang Fan, Xiukang Wang, Lifeng Wu, Hanmi Zhou, Fucang Zhang, Xiang Yu, Xianghui Lu, and Youzhen Xiang. “Comparison of Support Vector Machine and Extreme Gradient Boosting for predicting daily global solar radiation using temperature and precipitation in humid subtropical climates: A case study in China”. In: Energy conversion and management 164 (2018), pp. 102–111. [43] T Francke, JA López-Tarazón, and B Schröder. “Estimation of suspended sediment concentration and yield using linear models, random forests and quantile regression forests”. In: Hydrological Processes: An International Journal 22.25 (2008), pp. 4892–4904. [44] Meredith Franklin and Scott Fruin. “The role of traffic noise on the association between air pollution and children’s lung function”. In: Environmental research 157 (2017), pp. 153–159. [45] Meredith Franklin, Olga V Kalashnikova, and Michael J Garay. “Size-resolved particulate matter concentrations derived from 4.4 km-resolution size-fractionated Multi-angle Imaging SpectroRadiometer (MISR) aerosol optical depth over Southern California”. In: Remote Sensing of Environment 196 (2017), pp. 312–323. [46] Meredith Franklin, Hita Vora, Edward Avol, Rob McConnell, Fred Lurmann, Feifei Liu, Bryan Penfold, Kiros Berhane, Frank Gilliland, and W James Gauderman. “Predictors of intra-community variation in air quality”. In: Journal of exposure science & environmental epidemiology 22.2 (2012), pp. 135–147. [47] Meredith Franklin, Xiaozhe Yin, Rob McConnell, and Scott Fruin. “Association of the built environment with childhood psychosocial stress”. In: JAMA network open 3.10 (2020), e2017634–e2017634. [48] Laurence S Freedman, Arthur Schatzkin, Douglas Midthune, and Victor Kipnis. “Dealing with dietary measurement error in nutritional cohort studies”. In: Journal of theNational Cancer Institute 103.14 (2011), pp. 1086–1092. [49] Jerome Friedman, Trevor Hastie, and Robert Tibshirani. “Additive logistic regression: a statistical view of boosting (with discussion and a rejoinder by the authors)”. In: The annals of statistics 28.2 (2000), pp. 337–407. [50] Jerome H Friedman. “Greedy function approximation: a gradient boosting machine”. In: Annals of statistics (2001), pp. 1189–1232. [51] Naveen Garg and Sagar Maji. “A critical review of principal traffic noise models: Strategies and implications”. In: Environmental Impact Assessment Review 46 (2014), pp. 68–81. 119 [52] W James Gauderman, Edward Avol, Frank Gilliland, Hita Vora, Duncan Thomas, Kiros Berhane, Rob McConnell, Nino Kuenzli, Fred Lurmann, Edward Rappaport, et al. “The effect of air pollution on lung development from 10 to 18 years of age”. In: New England Journal of Medicine 351.11 (2004), pp. 1057–1067. [53] W James Gauderman, Hita Vora, Rob McConnell, Kiros Berhane, Frank Gilliland, Duncan Thomas, Fred Lurmann, Edward Avol, Nino Kunzli, Michael Jerrett, et al. “Effect of exposure to traffic on lung development from 10 to 18 years of age: a cohort study”. In: The Lancet 369.9561 (2007), pp. 571–577. [54] Natalia Genaro, Antonio Torija, A Ramos-Ridao, Ignacio Requena, Diego P Ruiz, and Montserrat Zamorano. “A neural network based model for urban noise prediction”. In: The journal of the Acoustical Society of America 128.4 (2010), pp. 1738–1746. [55] Sh Givargis and H Karimi. “A basic neural traffic noise prediction model for Tehran’s roads”. In: Journal of Environmental Management 91.12 (2010), pp. 2529–2534. [56] Holger R Goerlitz. “Weather conditions determine attenuation and speed of sound: Environmental limitations for monitoring and analyzing bat echolocation”. In: Ecology and evolution 8.10 (2018), pp. 5090–5100. [57] R Golmohammadi, M Abbaspour, P Nassiri, and H Mahjub. “A compact model for predicting road traffic noise”. In: Journal of Environmental Health Science & Engineering 6.3 (2009), pp. 181–186. [58] Gwenaël Guillaume, Pierre Aumond, Pierre Chobeau, and Arnaud Can. “Statistical study of the relationships between mobile and fixed stations measurements in urban environment”. In: Building and Environment 149 (2019), pp. 404–414. [59] Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Q Weinberger. “On calibration of modern neural networks”. In: International Conference on Machine Learning. PMLR. 2017, pp. 1321–1330. [60] Martin T Hagan, Howard B Demuth, and Mark Beale. Neural network design. PWS Publishing Co., 1997. [61] Khaled Hamad, Mohamad Ali Khalil, and Abdallah Shanableh. “Modeling roadway traffic noise in a hot climate using artificial neural networks”. In: TransportationResearch Part D: Transport and Environment 53 (2017), pp. 161–177. [62] Monica S Hammer, Tracy K Swinburn, and Richard L Neitzel. “Environmental noise pollution in the United States: developing an effective public health response”. In: Environmental health perspectives 122.2 (2014), pp. 115–119. 120 [63] Michael Hankard, Jeff Cerjan, and Joshua Leasure. Evaluation of the FHWA Traffic Noise Model, TNM, for Highway Traffic Noise Prediction in the State of Colorado . Tech. rep. Citeseer, 2006. [64] Otto Hänninen, Anne B Knol, Matti Jantunen, Tek-Ang Lim, André Conrad, Marianne Rappolder, Paolo Carrer, Anna-Clara Fanetti, Rokho Kim, Jurgen Buekers, et al. “Environmental burden of disease in Europe: assessing nine risk factors in six countries”. In: Environmental health perspectives 122.5 (2014), pp. 439–446. [65] KS Harishkumar, KM Yogesh, Ibrahim Gad, et al. “Forecasting air pollution particulate matter (PM2. 5) using machine learning regression models”. In: Procedia Computer Science 171 (2020), pp. 2057–2066. [66] Yaoyao He and Haiyan Li. “Probability density forecasting of wind power using quantile regression neural network and kernel density estimation”. In: Energy conversion and management 164 (2018), pp. 374–384. [67] Yaoyao He, Yang Qin, Shuo Wang, Xu Wang, and Chao Wang. “Electricity consumption probability density forecasting method based on LASSO-Quantile Regression Neural Network”. In: Applied energy 233 (2019), pp. 565–575. [68] Miyuki Hino, Elinor Benami, and Nina Brooks. “Machine learning for environmental monitoring”. In: Nature Sustainability 1.10 (2018), pp. 583–588. [69] Peter J Huber. “Robust regression: asymptotics, conjectures and Monte Carlo”. In: The annals of statistics (1973), pp. 799–821. [70] JT Gene Hwang and A Adam Ding. “Prediction intervals for artificial neural networks”. In: Journal of the American Statistical Association 92.438 (1997), pp. 748–757. [71] Hiral J Jariwala, Huma S Syed, Minarva J Pandya, and Yogesh M Gajera. “Noise Pollution & Human Health: A Review”. In: Indoor Built Environ (2017), pp. 1–4. [72] Nicholas E Johnson, Bartosz Bonczak, and Constantine E Kontokosta. “Using a gradient boosting model to improve the performance of low-cost aerosol monitors in a dense, heterogeneous urban environment”. In: Atmospheric environment 184 (2018), pp. 9–16. [73] Christoph Jung. “Offline-MapMatching–ein QGIS-Plug-in zum Abgleich einer Trajektorie mit einem Wegenetz”. In: J. Angew. Geoinf. 5 (2019), pp. 156–163. [74] HM Dipu Kabir, Abbas Khosravi, Mohammad Anwar Hosen, and Saeid Nahavandi. “Neural network-based uncertainty quantification: A survey of methodologies and applications”. In: IEEE access 6 (2018), pp. 36218–36234. [75] Marilena Kampa and Elias Castanas. “Human health effects of air pollution”. In: Environmental pollution 151.2 (2008), pp. 362–367. 121 [76] Yanghui Kang, Mutlu Ozdogan, Xiaojin Zhu, Zhiwei Ye, Christopher Hain, and Martha Anderson. “Comparative assessment of environmental variables and machine learning algorithms for maize yield prediction in the US Midwest”. In: Environmental Research Letters 15.6 (2020), p. 064005. [77] Ibrahim Karabayir, Samuel M Goldman, Suguna Pappu, and Oguz Akbilgic. “Gradient boosting for Parkinson’s disease diagnosis from voice recordings”. In: BMC Medical Informatics and Decision Making 20.1 (2020), pp. 1–7. [78] KS Kasiviswanathan and KP Sudheer. “Comparison of methods used for quantifying prediction interval in artificial neural network hydrologic models”. In: Modeling Earth Systems and Environment 2.1 (2016), p. 22. [79] KS Kasiviswanathan, KP Sudheer, Bankaru-Swamy Soundharajan, and Adebayo J Adeloye. “Implications of uncertainty in inflow forecasting on reservoir operation for irrigation”. In: Paddy and Water Environment 19.1 (2021), pp. 99–111. [80] Guolin Ke, Qi Meng, Thomas Finley, Taifeng Wang, Wei Chen, Weidong Ma, Qiwei Ye, and Tie-Yan Liu. “Lightgbm: A highly efficient gradient boosting decision tree”. In: Advances in neural information processing systems 30 (2017), pp. 3146–3154. [81] Abbas Khosravi, Saeid Nahavandi, Doug Creighton, and Amir F Atiya. “Comprehensive review of neural network-based prediction intervals and new advances”. In: IEEE Transactions on neural networks 22.9 (2011), pp. 1341–1356. [82] Roger Koenker and Gilbert Bassett Jr. “Regression quantiles”. In: Econometrica: journal of the Econometric Society (1978), pp. 33–50. [83] Naresh Kumar. “The exposure uncertainty analysis: the association between birth weight and trimester specific exposure to particulate matter (PM2. 5 vs. PM10)”. In: International journal of environmental research and public health 13.9 (2016), p. 906. [84] Paras Kumar, SP Nigam, and Narotam Kumar. “Vehicular traffic noise modeling using artificial neural network approach”. In: Transportation Research Part C: Emerging Technologies 40 (2014), pp. 111–122. [85] Sricharan Kumar and Ashok Srivastava. “Bootstrap prediction intervals in non-parametric regression with applications to anomaly detection”. In: Proc. 18th ACM SIGKDD Conf. Knowl. Discovery Data Mining. 2012. [86] Yuandu Lai, Yucheng Shi, Yahong Han, Yunfeng Shao, Meiyu Qi, and Bingshuai Li. “Exploring Uncertainty in Deep Learning for Construction of Prediction Intervals”. In: arXiv preprint arXiv:2104.12953 (2021). 122 [87] Charles E Land, Deukwoo Kwon, F Owen Hoffman, Brian Moroz, Vladimir Drozdovitch, André Bouville, Harold Beck, Nicholas Luckyanov, Robert M Weinstock, and Steven L Simon. “Accounting for shared and unshared dosimetric uncertainties in the dose response for ultrasound-detected thyroid nodules after exposure to radioactive fallout”. In: Radiation research 183.2 (2015), pp. 159–173. [88] Mark Landry, Thomas P Erlinger, David Patschke, and Craig Varrichio. “Probabilistic gradient boosting machines for GEFCom2014 wind forecasting”. In: International Journal of Forecasting 32.3 (2016), pp. 1061–1066. [89] Eunice Y Lee, Michael Jerrett, Zev Ross, Patricia F Coogan, and Edmund YW Seto. “Assessment of traffic-related noise in three cities in the United States”. In: Environmental research 132 (2014), pp. 182–189. [90] Bengang Li, Shu Tao, RW Dawson, Jun Cao, and Kinche Lam. “A GIS based road traffic noise prediction model”. In: Applied acoustics 63.6 (2002), pp. 679–691. [91] Jin Li, Andrew D Heap, Anna Potter, and James J Daniell. “Application of machine learning methods to spatial interpolation of environmental variables”. In: Environmental Modelling & Software 26.12 (2011), pp. 1647–1659. [92] Andy Liaw, Matthew Wiener, et al. “Classification and regression by randomForest”. In: R news 2.3 (2002), pp. 18–22. [93] Mark P Little, Deukwoo Kwon, Lydia B Zablotska, Alina V Brenner, Elizabeth K Cahoon, Alexander V Rozhko, Olga N Polyanskaya, Victor F Minenko, Ivan Golovanov, André Bouville, et al. “Impact of uncertainties in exposure assessment on thyroid cancer risk among persons in Belarus exposed as children or adolescents due to the Chernobyl accident”. In: PLoS One 10.10 (2015), e0139826. [94] Mengyang Liu, Hong Chen, Di Wei, Yunni Wu, and Chao Li. “Nonlinear relationship between urban form and street-level PM2. 5 and CO based on mobile measurements and gradient boosting decision tree models”. In: Building and Environment 205 (2021), p. 108265. [95] Shuo Liu, Youn-Hee Lim, Marie Pedersen, Jeanette T Jørgensen, Heresh Amini, Thomas Cole-Hunter, Amar J Mehta, Rina So, Laust H Mortensen, Rudi GJ Westendorp, et al. “Long-term air pollution and road traffic noise exposure and COPD: the Danish Nurse Cohort”. In: European Respiratory Journal 58.6 (2021). [96] Pablo Alvarez Lopez, Michael Behrisch, Laura Bieker-Walz, Jakob Erdmann, Yun-Pang Flötteröd, Robert Hilbrich, Leonhard Lücken, Johannes Rummel, Peter Wagner, and Evamarie Wießner. “Microscopic traffic simulation using sumo”. In: 2018 21st International Conference on Intelligent Transportation Systems (ITSC). IEEE. 2018, pp. 2575–2582. 123 [97] Jun Lu, Jinliang Ding, Xuewu Dai, and Tianyou Chai. “Ensemble stochastic configuration networks for estimating prediction intervals: A simultaneous robust training algorithm and its application”. In: IEEE transactions on neural networks and learning systems 31.12 (2020), pp. 5426–5440. [98] Tharsanee Maganathan, Soundariya Senthilkumar, and Vishnupriya Balakrishnan. “Machine Learning and Data Analytics for Environmental Science: A Review, Prospects and Challenges”. In: IOP Conference Series: Materials Science and Engineering. Vol. 955. 1. IOP Publishing. 2020, p. 012107. [99] A Masih. “Machine learning algorithms in air quality modeling”. In: Global Journal of Environmental Science and Management 5.4 (2019), pp. 515–534. [100] Shreedhar Maskey, Vincent Guinot, and Roland K Price. “Treatment of precipitation uncertainty in rainfall-runoff modelling: a fuzzy set approach”. In: Advances in water resources 27.9 (2004), pp. 889–898. [101] Dakota Aaron McCarty, Hyun Woo Kim, and Hye Kyung Lee. “Evaluation of light gradient boosted machine learning technique in large scale land use and land cover classification”. In: Environments 7.10 (2020), p. 84. [102] Rob McConnell, Kiros Berhane, Frank Gilliland, Stephanie J London, Talat Islam, W James Gauderman, Edward Avol, Helene G Margolis, and John M Peters. “Asthma in exercising children exposed to ozone: a cohort study”. In: The Lancet 359.9304 (2002), pp. 386–391. [103] Rob McConnell, Talat Islam, Ketan Shankardass, Michael Jerrett, Fred Lurmann, Frank Gilliland, Jim Gauderman, Ed Avol, Nino Künzli, Ling Yao, et al. “Childhood incident asthma and traffic-related air pollution at home and school”. In: Environmental health perspectives 118.7 (2010), pp. 1021–1026. [104] Reto Meier, Wayne E Cascio, Andrew J Ghio, Pascal Wild, Brigitta Danuser, and Michael Riediker. “Associations of short-term particle and noise exposures with markers of cardiovascular and respiratory health among highway maintenance workers”. In: Environmental health perspectives 122.7 (2014), pp. 726–732. [105] Nicolai Meinshausen and Greg Ridgeway. “Quantile regression forests.” In: Journal of Machine Learning Research 7.6 (2006). [106] Daniel R Nast, William S Speer, Colleen G Le Prell, et al. “Sound level measurements using smartphone" apps": Useful or inaccurate?” In: Noise and Health 16.72 (2014), p. 251. [107] Alexey Natekin and Alois Knoll. “Gradient boosting machines, a tutorial”. In: Frontiers in neurorobotics 7 (2013), p. 21. 124 [108] Vladimir Nedic, Danijela Despotovic, Slobodan Cvetanovic, Milan Despotovic, and Sasa Babic. “Comparison of classical statistical methods and artificial neural network in traffic noise prediction”. In: Environmental Impact Assessment Review 49 (2014), pp. 24–30. [109] Richard L Neitzel, Robyn RM Gershon, Tara P McAlexander, Lori A Magda, and Julie M Pearson. “Exposures to transit and other sources of noise among New York City residents”. In: Environmental science & technology 46.1 (2012), pp. 500–508. [110] Hildegard Niemann, Xavier Bonnefoy, Matthias Braubach, Karl Hecht, Christian Maschke, C Rodrigues, Nathalie Robbel, et al. “Noise-induced annoyance and morbidity results from the pan-European LARES study”. In: Noise and Health 8.31 (2006), p. 63. [111] Vahid Nourani, Nardin Jabbarian Paknezhad, and Hitoshi Tanaka. “Prediction Interval Estimation Methods for Artificial Neural Network (ANN)-Based Modeling of the Hydro-Climatic Processes, a Review”. In: Sustainability 13.4 (2021), p. 1633. [112] Yasuaki Okada, Koichi Yoshihisa, and Kenji Tatsuda. “Annual fluctuation of atmospheric absorption of sound in various world regions”. In: Acoustical Science and Technology 37.2 (2016), pp. 66–74. [113] Wen-Tsao Pan, Chiung-En Huang, and Chiung-Lin Chiu. “Study on the performance evaluation of online teaching using the quantile regression analysis and artificial neural network”. In: The Journal of Supercomputing 72.3 (2016), pp. 789–803. [114] Tim Pearce, Alexandra Brintrup, Mohamed Zaki, and Andy Neely. “High-quality prediction intervals for deep learning: A distribution-free, ensembled approach”. In: International Conference on Machine Learning. PMLR. 2018, pp. 4075–4084. [115] John M Peters, Edward Avol, William Navidi, Stephanie J London, W James Gauderman, Fred Lurmann, William S Linn, Helene Margolis, Edward Rappaport, Henry Gong Jr, et al. “A study of twelve Southern California communities with differing levels and types of air pollution: I. Prevalence of respiratory morbidity”. In: American journal of respiratory and critical care medicine 159.3 (1999), pp. 760–767. [116] Sandra Pirrera, Elke De Valck, and Raymond Cluydts. “Nocturnal road traffic noise: A review on its assessment and consequences on sleep and health”. In: Environment international 36.5 (2010), pp. 492–498. [117] Novi Quadrianto and Zoubin Ghahramani. “A very simple safe-Bayesian random forest”. In: IEEE transactions on pattern analysis and machine intelligence 37.6 (2014), pp. 1297–1303. 125 [118] Guillermo Quintero, Pierre Aumond, Arnaud Can, Andreu Balastegui, and Jordi Romeu. “Statistical requirements for noise mapping based on mobile measurements using bikes”. In: Applied Acoustics 156 (2019), pp. 271–278. [119] ME Ramazani, M Mosaferi, Y Rasoulzadeh, M Pourakbar, MA Jafarabadi, and H Amini. “Temporal and spatial evaluation of environmental noise in urban area: a case study in Iran”. In: International Journal of Environmental Science and Technology 15.6 (2018), pp. 1179–1192. [120] Alberto Recio, Cristina Linares, José Ramón Banegas, and Julio Dıáz. “Road traffic noise effects on cardiovascular, respiratory, and metabolic health: An integrative model of biological mechanisms”. In: Environmental research 146 (2016), pp. 359–370. [121] Jennifer Richmond-Bryant and Thomas C Long. “Influence of exposure measurement errors on results from epidemiologic studies of different designs”. In: Journal of Exposure Science & Environmental Epidemiology 30.3 (2020), pp. 420–429. [122] Ryan Rifkin and Aldebaro Klautau. “In defense of one-vs-all classification”. In: The Journal of Machine Learning Research 5 (2004), pp. 101–141. [123] Erin A Riley, LaNae Schaal, Miyoko Sasakura, Robert Crampton, Timothy R Gould, Kris Hartin, Lianne Sheppard, Timothy Larson, Christopher D Simpson, and Michael G Yost. “Correlations between short-term mobile monitoring and long-term passive sampler measurements of traffic-related air pollution”. In: Atmospheric Environment 132 (2016), pp. 229–239. [124] Hunjae Ryu, In Kwon Park, Bum Seok Chun, and Seo Il Chang. “Spatial statistical analysis of the effects of urban form indicators on road-traffic noise exposure of a city in South Korea”. In: Applied acoustics 115 (2017), pp. 93–100. [125] George Arthur Frederick Saber and Christopher Johncoaut Wild. Nonlinear regression. Tech. rep. 1989. [126] Emrehan Kutlug Sahin. “Comparative analysis of gradient boosting algorithms for landslide susceptibility mapping”. In: Geocarto International (2020), pp. 1–25. [127] Evangelia Samoli, Barbara K Butland, Sophia Rodopoulou, Richard W Atkinson, Benjamin Barratt, Sean D Beevers, Andrew Beddows, Konstantina Dimakopoulou, Joel D Schwartz, Mahdieh Danesh Yazdi, et al. “The impact of measurement error in modeled ambient particles exposures on health effect estimates in multilevel analysis: A simulation study”. In: Environmental Epidemiology 4.3 (2020). [128] Jeong C Seong, Tae H Park, Joon H Ko, Seo I Chang, Minho Kim, James B Holt, and Mohammed R Mehdi. “Modeling of road traffic noise and estimated human exposure in Fulton County, Georgia, USA”. In: Environment international 37.8 (2011), pp. 1336–1341. 126 [129] Robert P Sheridan, Andy Liaw, and Matthew Tudor. “Light Gradient Boosting Machine as a Regression Method for Quantitative Structure-Activity Relationships”. In: arXiv preprint arXiv:2105.08626 (2021). [130] Masoud Fallah Shorshani, Michel André, Céline Bonhomme, and Christian Seigneur. “Modelling chain for the effect of road traffic on air and water quality: Techniques, current status and future prospects”. In: Environmental Modelling & Software 64 (2015), pp. 102–123. [131] Ning Shu, Louis F. Cohn, Roswell A. Harris, Teak K. Kim, and Wensheng Li. “Comparative evaluation of the ground reflection algorithm in FHWA Traffic Noise Model (TNM 2.5)”. In: Applied Acoustics 68.11 (2007), pp. 1459–1467.doi: https://doi.org/10.1016/j.apacoust.2006.07.004. [132] Minxing Si and Ke Du. “Development of a predictive emissions model using a gradient boosting machine learning method”. In: Environmental Technology & Innovation 20 (2020), p. 101028. [133] Daljeet Singh, SP Nigam, VP Agrawal, and Maneek Kumar. “Vehicular traffic noise prediction using soft computing approach”. In: Journal of environmental management 183 (2016), pp. 59–66. [134] Stephen A Stansfeld. “Noise effects on health in the context of air pollution exposure”. In: International journal of environmental research and public health 12.10 (2015), pp. 12735–12760. [135] Stephen A Stansfeld, Birgitta Berglund, Charlotte Clark, Isabel Lopez-Barrio, Peter Fischer, Evy Öhrström, Mary M Haines, Jenny Head, Staffan Hygge, Irene Van Kamp, et al. “Aircraft and road traffic noise and children’s cognition and health: a cross-national study”. In: The Lancet 365.9475 (2005), pp. 1942–1949. [136] Campbell Steele. “A critical review of some traffic noise prediction models”. In: Applied acoustics 62.3 (2001), pp. 271–287. [137] Yuelai Su. “Prediction of air quality based on Gradient Boosting Machine Method”. In: 2020 International Conference on Big Data and Informatization Education (ICBDIE). IEEE. 2020, pp. 395–397. [138] James W Taylor. “A quantile regression neural network approach to estimating the conditional density of multiperiod returns”. In: Journal of Forecasting 19.4 (2000), pp. 299–311. [139] Robert Tibshirani. “A comparison of some error estimates for neural network models”. In: Neural Computation 8.1 (1996), pp. 152–163. 127 [140] Carla MT Tiesler, Matthias Birk, Elisabeth Thiering, Gabriele Kohlböck, Sibylle Koletzko, Carl-Peter Bauer, Dietrich Berdel, Andrea von Berg, Wolfgang Babisch, Joachim Heinrich, et al. “Exposure to road traffic noise and children’s behavioural problems and sleep disturbance: results from the GINIplus and LISAplus studies”. In: Environmental research 123 (2013), pp. 1–8. [141] Samir Touzani, Jessica Granderson, and Samuel Fernandes. “Gradient boosting machine for modeling the energy consumption of commercial buildings”. In: Energy and Buildings 158 (2018), pp. 1533–1543. [142] Robert Urman, Rob McConnell, Talat Islam, Edward L Avol, Frederick W Lurmann, Hita Vora, William S Linn, Edward B Rappaport, Frank D Gilliland, and W James Gauderman. “Associations of children’s lung function with ambient air pollution: joint effects of regional and near-roadway pollutants”. In: Thorax 69.6 (2014), pp. 540–547. [143] Kévin Vaysse and Philippe Lagacherie. “Using quantile regression forest to estimate uncertainty of digital soil mapping products”. In: Geoderma 291 (2017), pp. 55–64. [144] Hadrien Verbois, Andrivo Rusydi, and Alexandre Thiery. “Probabilistic forecasting of day-ahead solar irradiance using quantile gradient boosting”. In:Solar Energy 173 (2018), pp. 313–327. [145] Alva Enoksson Wallas, Charlotta Eriksson, Mikael Ögren, Andrei Pyko, Mattias Sjöström, Erik Melén, Göran Pershagen, and Olena Gruzieva. “Noise exposure and childhood asthma up to adolescence”. In: Environmental research 185 (2020), p. 109404. [146] Ching-Yun Wang and Xiao Song. “Robust best linear estimator for Cox regression with instrumental variables in whole cohort and surrogates with additive measurement error in calibration sample”. In: Biometrical Journal 58.6 (2016), pp. 1465–1484. [147] Haibo Wang, Ming Cai, and Hongjun Cui. “Simulation and analysis of road traffic noise among urban buildings using spatial subdivision-based beam tracing method”. In: International journal of environmental research and public health 16.14 (2019), p. 2491. [148] Haibo Wang, Huimin Gao, and Ming Cai. “Simulation of traffic noise both indoors and outdoors based on an integrated geometric acoustics method”. In: Building and Environment 160 (2019), p. 106201. [149] Garrett M Weaver and W James Gauderman. “Traffic-related pollutants: exposure and health effects among Hispanic children”. In: American journal of epidemiology 187.1 (2018), pp. 45–52. 128 [150] Jing Wei, Zhanqing Li, Rachel T Pinker, Jun Wang, Lin Sun, Wenhao Xue, Runze Li, and Maureen Cribb. “Himawari-8-derived diurnal variations in ground-level PM 2.5 pollution across China using the fast space-time Light Gradient Boosting Machine (LightGBM)”. In: Atmospheric Chemistry and Physics 21.10 (2021), pp. 7863–7880. [151] Yaguang Wei, Xinye Qiu, Mahdieh Danesh Yazdi, Alexandra Shtein, Liuhua Shi, Jiabei Yang, Adjani A Peralta, Brent A Coull, and Joel D Schwartz. “The impact of exposure measurement error on the estimated concentration–response relationship between long-term exposure to PM 2.5 and mortality”. In: Environmental Health Perspectives 130.7 (2022), p. 077006. [152] Po-Jiun Wen and Chihpin Huang. “Noise prediction using machine learning with measurements analysis”. In: Applied Sciences 10.18 (2020), p. 6619. [153] Christopher K Williams and Carl Edward Rasmussen. Gaussian processes for machine learning. Vol. 2. 3. MIT press Cambridge, MA, 2006. [154] You Wu, F Owen Hoffman, A Iulian Apostoaei, Deukwoo Kwon, Brian A Thomas, Racquel Glass, and Lydia B Zablotska. “Methods to account for uncertainties in exposure assessment in studies of environmental exposures”. In: Environmental Health 18.1 (2019), pp. 1–15. [155] Dan Xie, Yi Liu, and Jining Chen. “Mapping urban environmental noise: a land use regression method”. In: Environmental science & technology 45.17 (2011), pp. 7358–7364. [156] Qifa Xu, Kai Deng, Cuixia Jiang, Fang Sun, and Xue Huang. “Composite quantile regression neural network with applications”. In: Expert Systems with Applications 76 (2017), pp. 129–139. [157] Xiaozhe Yin, Masoud Fallah-Shorshani, Rob McConnell, Scott Fruin, and Meredith Franklin. “Predicting fine spatial scale traffic noise using mobile measurements and machine learning”. In: Environmental Science & Technology 54.20 (2020), pp. 12860–12869. [158] Michael A Yonas, Nancy E Lange, and Juan C Celedón. “Psychosocial stress and asthma morbidity”. In: Current opinion in allergy and clinical immunology 12.2 (2012), p. 202. [159] Keming Yu, Zudi Lu, and Julian Stander. “Quantile regression: applications and current research areas”. In: Journal of the Royal Statistical Society: Series D (The Statistician) 52.3 (2003), pp. 331–350. [160] Mehdi Zamani Joharestani, Chunxiang Cao, Xiliang Ni, Barjeece Bashir, and Somayeh Talebiesfandarani. “PM2. 5 prediction based on random forest, XGBoost, and deep learning using multisource remote sensing data”. In: Atmosphere 10.7 (2019), p. 373. 129 [161] Tianning Zhang, Weihuan He, Hui Zheng, Yaoping Cui, Hongquan Song, and Shenglei Fu. “Satellite-based ground PM2. 5 estimation using a gradient boosting decision tree”. In: Chemosphere 268 (2021), p. 128801. [162] Shifa Zhong, Kai Zhang, Majid Bagheri, Joel G Burken, April Gu, Baikun Li, Xingmao Ma, Babetta L Marrone, Zhiyong Jason Ren, Joshua Schrier, et al. “Machine learning: new ideas and tools in environmental science and engineering”. In: Environmental Science & Technology 55.19 (2021), pp. 12741–12754. [163] Jian Zhou, Enming Li, Shan Yang, Mingzheng Wang, Xiuzhi Shi, Shu Yao, and Hani S Mitri. “Slope stability prediction for circular mode failure using gradient boosting machine approach based on an updated database of case histories”. In: Safety Science 118 (2019), pp. 505–518. [164] Enrico Zio. “A study of the bootstrap method for estimating the accuracy of artificial neural networks in predicting nuclear transient processes”. In: IEEE Transactions on Nuclear Science 53.3 (2006), pp. 1460–1478. 130

Abstract (if available)

Abstract Environmental noise has been associated with a variety of health endpoints including cardiovascular disease, sleep disturbance, depression, and psychosocial stress. Most population noise exposure comes from vehicular traffic, which has large fine-scale spatial variability that is difficult to characterize using traditional fixed-site measurement techniques. To address this challenge, we collected A-weighted, equivalent noise (LAeq in decibels, dB) data on hour-long foot journeys around 16 locations throughout Long Beach, CA, and trained four machine learning models, linear regression, random forest, extreme gradient boosting, and a neural network to predict noise with 20 m resolution. Input variables to the models included traffic metrics, road network features, meteorological conditions, and land use type. Among all machine learning models, extreme gradient boosting had the best results in validation tests (leave-one-route-out R2 = 0.71, root mean square error (RMSE) 4.54 dB; 5-fold R2 = 0.96, RMSE 1.8 dB). Local traffic volume was the most important predictor of noise; road features, land use, and meteorology including humidity, temperature, and wind speed also contributed. We show that a novel, on-foot mobile noise measurement method coupled with machine learning approaches enables highly accurate predictions of small-scale spatial patterns in traffic-related noise over a mixed-use urban area.
Estimating uncertainty in exposure model predictions is an underutilized but potentially important metric in environmental epidemiological studies. Failure to account for uncertainty can lead to biased results in exposure-response analyses. Given the recent popularity of machine learning methods such as Extreme Gradient Boosting (XGBoost) for exposure modeling, where uncertainty determinations are still not standardized, uncertainty analysis is an area deserving of greater attention. We propose enhancements to XGBoost whereby a modified quantile regression is used as the objective function in order to estimate uncertainty (QXGBoost). Specifically, we included the Huber norm in the quantile regression model to construct a differentiable approximation to the quantile regression error function. This key step allows the gradient-based optimization algorithm in XGBoost to make probabilistic predictions more efficiently and improve the efficiency of finding the optimal gradient descent rates for rapid solutions. These techniques were then applied to create 90% prediction intervals for one simulated dataset and a real-life environmental dataset of measured traffic noise.
For all two datasets, QXGBoost had better model performance compared to regular quantile gradient boosting and quantile light gradient boosting. In the test datasets, almost 90% of the observations lay within the prediction intervals using QXGBoost. For the simulated and traffic noise datasets, the quality of the prediction intervals from QXGBoost was better than the other models. Thus, compared to other methods, our prediction intervals using QXGBoost show better performance metrics.
Uncertainty estimates of traffic noise, central site PM2.5, and freeway and non-freeway emission concentrations of oxides of nitrogen (NOx, ppb) were spatially assigned to children in Long Beach who were tested for forced vital capacity (FVC) and forced expiratory volume in 1 second, (FEV1). The associations between traffic related air pollution and these outcomes, with and without adjustment for noise, were examined using mixed effects models. To account for the uncertainties of traffic noise, different numbers of intensive simulations were drawn within the lower and upper bound of the prediction intervals using both uniform and Gaussian sampling methods. The generated traffic noise variables were then fit iteratively in the mixed effects models to examine their average effect on the associations between traffic-related air pollution and FEV1 and FVC. Overall, traffic noise with or without uncertainty did not confound the association between PM2.5 and lung function. Traffic noise without uncertainty confounded 36.0% and 18.3% of the association between freeway NOx and FEV1 and FVC, respectively, and 59.2% and 62.9% for non-freeway NOx. After accounting for uncertainty, the confounding effects were reduced to 14% and 6.7% between freeway NOx and FEV1 and FVC, and 31.4% and 34.1% between freeway NOx and FEV1 and FVC. The confounding effect of traffic noise is diminished after accounting for uncertainty.
Our results indicated that failure to account for uncertainties in exposure estimation may lead to underestimation of the effect of exposures in epidemiological studies. Gaussian sampling methods could give results closer to those without accounting for uncertainty. Usually, a large number of simulations could give better and more robust results, but it also depends on the data.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Covariance-based distance-weighted regression for incomplete and misaligned spatial data

PDF

Spatial modeling of non-tailpipe emissions and its association with children's lung function

PDF

Evaluation of new methods for estimating exposure to traffic-related pollution and early health effects for large population epidemiological studies

PDF

Disparities in exposure to traffic-related pollution sources by self-identified and ancestral Hispanic descent in participants of the USC Children’s Health Study

PDF

Machine learning approaches for downscaling satellite observations of dust

PDF

Using multi-angle imaging spectroradiometer aerosol mixture properties and meteorology for PM₂.₅ assessment in Iran

PDF

Comparison of models for predicting PM2.5 concentration in Wuhan, China

PDF

Examining exposure to extreme heat and air pollution and its effects on all-cause, cardiovascular, and respiratory mortality in California: effect modification by the social deprivation index

PDF

Associations of ambient air pollution exposures with perceived stress in the MADRES cohort

Asset Metadata

Creator Yin, Xiaozhe (author)

Core Title Uncertainty quantification in extreme gradient boosting with application to environmental epidemiology

School Keck School of Medicine

Degree Doctor of Philosophy

Degree Program Biostatistics

Degree Conferral Date 2022-12

Publication Date 09/22/2022

Defense Date 08/15/2022

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag environmental epidemiology,exposure estimation,machine learning,OAI-PMH Harvest,quantile regression,spatial statistics,traffic noise,uncertainty,XGBoost

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Franklin, Meredith (committee chair), Chiang, Yao-Yi (committee member), Fruin, Scott (committee member), Lewinger, Juan Pablo (committee member), McConnell, Rob (committee member)

Creator Email xiaozhey@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC112023346

Unique identifier UC112023346

Legacy Identifier etd-YinXiaozhe-11229

Document Type Dissertation

Format application/pdf (imt)

Rights Yin, Xiaozhe

Internet Media Type application/pdf

Type texts

Source 20220925-usctheses-batch-984 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu