Partial Dependence Plots Research Articles

Introduction: Predictive analytics powered by artificial intelligence (AI) and machine learning (ML) are revolutionizing cardiovascular risk assessment. Accurate prediction of low-density lipoprotein cholesterol (LDL-C) is critical for evaluating cardiovascular disease (CVD) risk and guiding therapeutic decisions. This study evaluates deep learning (DL) models for LDL-C prediction in patients with prior cardiovascular events, comparing their performance against traditional ML methods and established LDL-C estimation formulas. Methods: We retrospectively analyzed data from 8,315 patients with documented cardiovascular events from Rhythm Heart and Critical Care. Key lipid parameters included LDL-C, triglycerides (TG), total cholesterol (TC), and high-density lipoprotein cholesterol (HDL-C). Patient CVD history was blinded during model training to ensure unbiased prediction. DL models tested included Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN), Long Short-Term Memory (LSTM) networks, and a Transformer-based architecture. These were benchmarked against Back Propagation Neural Network (BPNN) models and LDL-C formulas by Sampson and Martin. Model performance was assessed using Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE). Results: The models generated LDL-C predictions for 5,132 patients (61% of the cohort). The Transformer-based model achieved the highest accuracy with an RMSE of 10.58 mg/dL and MAPE of 7.35%, significantly outperforming BPNN (RMSE 17.16 mg/dL; MAPE 11.01%), RNN (RMSE 32.47 mg/dL), and LSTM (RMSE 32.51 mg/dL). Deep learning models also surpassed traditional LDL-C formulas in accuracy. Partial Dependence Plots (PDP) of the Transformer model revealed clinically meaningful relationships between LDL-C and predictors such as HDL-C, BMI, and thyroid hormones, supporting physiological validity and interpretability. Conclusion: This study demonstrates that DL models, particularly the Transformer-based approach, significantly outperform conventional methods in predicting LDL-C levels among patients with cardiovascular events. The model’s superior accuracy and interpretability offer a promising clinical tool for personalized risk assessment, early detection, and optimized management of CVD. Incorporation of such AI-driven models into clinical workflows could improve patient outcomes and resource allocation in cardiovascular care.

Pitfalls in machine learning interpretability: Manipulating partial dependence plots to hide discrimination

Assessment of Global Planted-to-Natural Mangroves Biomass Ratio and Mangroves Biomass Carbon Stocks by Machine Learning.

Hierarchical machine learning-based prediction for ultrasonic degradation of organic pollutants using sonocatalysts.

ABSTRACTWith the spread and rapid advancement of black box machine learning (ML) models, the field of interpretable machine learning (IML) or explainable artificial intelligence (XAI) has become increasingly important over the last decade. This is particularly relevant for survival analysis, where the adoption of IML techniques promotes transparency, accountability, and fairness in sensitive areas, such as clinical decision‐making processes, the development of targeted therapies, interventions, or in other medical or healthcare‐related contexts. More specifically, explainability can uncover a survival model's potential biases and limitations and provide more mathematically sound ways to understand how and which features are influential for prediction or constitute risk factors. However, the lack of readily available IML methods may have deterred practitioners from leveraging the full potential of ML for predicting time‐to‐event data. We present a comprehensive review of the existing work on IML methods for survival analysis within the context of the general IML taxonomy. In addition, we formally detail how commonly used IML methods, such as individual conditional expectation (ICE), partial dependence plots (PDP), accumulated local effects (ALE), different feature importance measures, or Friedman's H‐interaction statistics can be adapted to survival outcomes. An application of several IML methods to data on breast cancer recurrence in the German Breast Cancer Study Group (GBSG2) serves as a tutorial or guide for researchers, on how to utilize the techniques in practice to facilitate understanding of model decisions or predictions.

ABSTRACT This study advances governance scholarship by applying robust machine learning techniques, bagging, random forest, boosting, SHapley Additive exPlanations (SHAP), and partial dependence plots (PDPs), to systematically explore how diverse board compositions (gender diversity, nonexecutive member diversity, independent board diversity) and the presence of board members with specific strategic skills (board‐specific skills percent) impact firms' environmental innovation outcomes. Using comprehensive governance data from the hospitality and tourism sector (Refinitiv, 2015–2024), results reveal strong predictive relationships, highlighting product responsibility as the most influential factor. The analysis further indicates that board‐specific skills and external diversity significantly amplify firms' environmental innovation, particularly when combined with proactive sustainability practices. SHAP and PDP analyses provide deeper insights into these nonlinear interactions, enriching theoretical perspectives drawn from Resource Dependency Theory, Upper Echelons Theory, and Stakeholder Theory. This study offers valuable strategic implications for industry practitioners aiming to leverage targeted governance structures to enhance sustainability‐driven innovation.

Abstract Background The use of incinerated bottom ash (IBA) as a sustainable construction material offers potential environmental benefits but introduces complex interactions with cement chemistry. Magnesium phosphate cement (MPC), known for its rapid hardening and superior bonding, can be optimized through the controlled incorporation of IBA. However, limited studies have addressed how the chemical components of IBA affect the compressive strength of MPC, particularly using data-driven approaches. Methods A database of 396 experimental samples was compiled from previous studies considering mix proportions, oxide compositions, and curing conditions. Four ensemble machine learning algorithms—Extreme Gradient Boosting (XGB), Light Gradient Boosting (LGB), Gradient Boosting Regressor (GBR), and Random Forest (RFR)—were employed to predict compressive strength. Model robustness was validated through 5-fold cross-validation. Feature interpretation was achieved using SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP) to quantify individual and interactive effects of chemical and physical parameters. Results The XGB model achieved the highest predictive accuracy, with mean training and testing R2 values greater than 0.90 and 0.80, and the lowest mean absolute percentage error of 16.71%. SHAP analysis identified curing age as the most dominant factor, followed by FA/C, W/C, and MgO/PO4 ratios. IBA content and specific oxides such as Fe2O3 and Al2O3 contributed positively to strength within optimal ranges. PDP confirmed nonlinear dependencies, indicating a 26% reduction in strength as W/C increased from 0.1 to 0.6, while extended curing up to 28 days improved performance substantially. Conclusion The integration of SHAP and PDP provided a transparent interpretation of feature interactions in IBA-modified MPC. The developed XGB model demonstrated strong generalization and interpretability. The combined modeling approach offers a reliable predictive framework for optimizing IBA incorporation in sustainable binder systems and advancing eco-efficient material design.

PurposeTo develop predictive models for postoperative visual acuity—both near and distance, monocular and binocular—and a composite outcome metric, distance-corrected visual gain (DCVG), in patients undergoing presbyopic corneal refractive surgery.MethodsA retrospective analysis was performed on 914 eyes from 457 patients treated with PresbyMAX who completed 6 months of follow-up. Machine learning algorithms, including Random Forest regression and classification models, were applied to predict corrected distance visual acuity (CDVA) and distance-corrected near visual acuity (DCNVA), both measured using the same distance correction. Feature importance was evaluated using Shapley additive explanations (SHAP) and partial dependence plots (PDPs).ResultsBinocular models outperformed monocular in predictive accuracy, and CDVA was more predictable than DCNVA. A clinical trade-off was observed whereby improvements of up to three lines in DCNVA could be achieved without significant CDVA loss. The optimal planned addition ranged between +1.50 D and +2.25 D, balancing near and distance vision outcomes. Patients 45 to 56 years of age showed greater potential for near vision gain without compromising distance vision. The DCVG metric effectively quantified overall visual benefits, with only a minority of cases showing a net loss.ConclusionsPredictive modeling combined with the DCVG metric enables personalized surgical planning by identifying key factors influencing outcomes. This approach supports better management of the visual trade-offs inherent in presbyopic refractive surgery.Translational RelevanceMachine learning–based prediction models and the DCVG metric facilitate individualized clinical decision-making, improving patient counseling and optimizing the balance between near and distance vision in presbyopic treatment.

Ovarian cancer’s high mortality is primarily due to late-stage diagnosis, underscoring the critical need for improved early detection tools. This study develops and validates explainable artificial intelligence (XAI) models to discriminate malignant from benign ovarian masses using readily available demographic and laboratory data. A dataset of 309 patients (140 malignant, 169 benign) with 47 clinical parameters was analyzed. The Boruta algorithm selected 19 significant features, including tumor markers (CA125, HE4, CEA, CA19-9, AFP), hematological indices, liver function tests, and electrolytes. Five ensemble machine learning algorithms were optimized and evaluated using repeated stratified 5-fold cross-validation. The Gradient Boosting model achieved the highest performance with 88.99% (±3.2%) accuracy, 0.934 AUC-ROC, and 0.782 Matthews correlation coefficient. SHAP analysis identified HE4, CEA, globulin, CA125, and age as the most globally important features. Unlike black-box approaches, our XAI framework provides clinically interpretable decision pathways through LIME and SHAP visualizations, revealing how feature values push predictions toward malignancy or benignity. Partial dependence plots illustrated non-linear risk relationships, such as a sharp increase in malignancy probability with CA125 > 35 U/mL. This explainable approach demonstrates that ensemble models can achieve high diagnostic accuracy using routine lab data alone, performing comparably to established clinical indices while ensuring transparency and clinical plausibility. The integration of state-of-the-art XAI techniques highlights established biomarkers and reveals potential novel contributors like inflammatory and hepatic indices, offering a pragmatic, scalable triage tool to augment existing diagnostic pathways, particularly in resource-constrained settings.

Generative physics-informed machine learning for modeling indoor air quality and its impact on student health and performance.

This study aims to enhance the explainability and predictive accuracy of the Random Survival Forest (RSF) algorithm in predicting stent patency risk for patients with malignant colonic obstruction. The RSF algorithm was applied to clinical prognostic data of 109 patients with malignant colonic obstruction who underwent self-expandable metallic stent (SEMS) procedures between September 2014 and October 2023. We combined the RSF variable importance and Least Absolute Shrinkage and Selection Operator (Lasso) regression to identify the final predictive variables. And the performance of the RSF model was compared with the Cox Proportional Hazards (CPH) model using both global and local explanation methods. The RSF model demonstrated superior predictive performance, with higher time-dependent AUCs and lower Brier scores compared to the CPH model across various time points. Significant predictors of stent patency identified by the RSF and Lasso models included Diabetes, CA199, Pre-Chemotherapy and Length of obstruction. The partial dependence plots highlighted CA199 and Length of obstruction as critical variables, with SHAP (SHapley Additive exPlanations) and LIME (Local Interpretable Model-agnostic Explanations) analyses further revealing the dynamic, time-varying impact of these variables on individual patient outcomes. The RSF algorithm, supplemented with comprehensive feature importance analyses and advanced interpretability techniques, offers a robust and reliable framework for predicting stent patency risk in patients with malignant colonic obstruction.

In critically ill patients, a discrepancy frequently exists between percutaneous oxygen saturation (SpO₂) and arterial blood oxygen saturation (SaO₂), which can lead to potential hypoxemia being overlooked. The aim of this study was to explore the factors related to the discrepancy and to develop an easy-to-use prediction model that uses readily available bedside information to predict the discrepancy and suggest the need for arterial blood gas measurement. This is a prognostic study that used eICU Collaborative Research Database from 2014 to 2015 for model development and MIMIC-IV data from 2008 to 2019 for model validation. To predict the outcome of SpO₂ exceeding SaO₂ by 3% or more, non-invasive, readily available bedside information (patient demographics, vital signs, vasopressor use, ventilator use) was used to develop prediction models with three machine learning methods (decision tree, logistic regression, XGBoost). To make the model accessible, the model was deployed as a web-based application. Additionally, the contribution of each variable was explored using partial dependence plots and SHAP values. From 4,781 admission records in eICU data, a total of 19,804 paired SpO₂ and SaO₂ measurements were used. Among three machine learning models, the XGBoost model demonstrated the best predictive performance with an AUROC of 0.73 and a calibration slope of 0.90. In the validation cohort of MIMIC-IV paired dataset, the performance was AUROC of 0.56. An exploratory model-updating step followed by temporal validation raised performance to AUROC of 0.70 with a calibration slope of 0.85. In both datasets, worse vital signs were associated with the discrepancy (e.g., low blood pressure, low temperature) between SpO₂ and SaO₂. Using non-invasive bedside data, a machine learning model was developed to predict SpO₂-SaO₂ discrepancy and identified vital signs as key contributors. These findings underscore the awareness for hidden hypoxemia and provide the basis of further study to accurately evaluate the actual SaO₂.

Abstract To overcome the limitations of conventional single‐factor analysis, this study proposed a framework for investigating interaction effects of influencing factors on the resilient modulus (Mr) of stabilized aggregate base. First, cross‐validation was utilized to compare the predictive accuracy and generalization capability of gradient boosting (GB) and random forest (RF) in predicting the Mr. The grid search algorithm was used to optimize hyperparameters. After optimization, the coefficient of determination for GB reached 0.99 on the training set and 0.96 on the test set, while those for RF were 0.98 and 0.94, respectively. The results indicated that GB demonstrated higher predictive accuracy for the Mr. Finally, the importance analysis, univariate sensitivity analysis, and bivariate interaction sensitivity analysis of influencing factors were systematically conducted using partial dependence plots (PDP) and Shapley additive explanations (SHAP). The research results showed that the importance of influencing factors on the Mr decreases in the order of maximum dry density to optimum moisture content ratio, wet–dry cycles (WDC), deviator stress, confining pressure, and ratio of oxide compounds in the cementitious materials. The bivariate interaction sensitivity analysis of the WDC, deviator stress, confining pressure, and ratio of oxide compounds in the cementitious materials did not disrupt their single‐variable sensitivity relationships with the Mr. The variation of the WDC would destroy the single variable sensitivity relationship between the optimum moisture content ratio and Mr.

Enhancing interlayer bond strength remains a critical challenge in the extrusion-based 3D printing of cementitious materials. This study investigates the optimisation of interlayer bond strength in extrusion-based 3D-printed cementitious materials through a combined application of Response Surface Methodology (RSM) and Artificial Neural Networks (ANNs). Using a concise yet comprehensive dataset, RSM provided interpretable main effects, curvature, and interactions, while the ANN captured non-linearities beyond quadratic forms. Comparative analysis revealed that the RSM model achieved higher predictive accuracy (R2=0.95) compared to the ANN model (R2=0.87). Desirability-based optimisation confirmed the critical importance of minimising casting delays to mitigate interlayer weaknesses, with RSM suggesting a water-to-cement (W/C) ratio of approximately 0.45 and a minimal time gap of less than 5 min, while ANN predicted slightly lower optimal W/C values but with reduced reliability due to the limited dataset. Sensitivity analysis using partial dependence plots (PDPs) further highlighted that ordinary Portland cement (OPC) content and W/C ratio are the dominant factors, contributing approximately 2.0 and 1.8 MPa respectively to the variation in predicted bond strength, followed by superplasticiser dosage and silica content. Variables such as water content, viscosity-modifying agent, and time gap exhibited moderate influence, while sand and fibre content had marginal effects within the tested ranges. These results demonstrate that RSM provides robust predictive performance and interpretable optimisation guidance, while ANN offers flexible non-linear modelling but requires larger datasets to achieve stable generalisation. Integrating both methods offers a complementary pathway to advance mix design and process control strategies in 3D concrete printing.

In critically ill patients, a discrepancy frequently exists between percutaneous oxygen saturation (SpO₂) and arterial blood oxygen saturation (SaO₂), which can lead to potential hypoxemia being overlooked. The aim of this study was to explore the factors related to the discrepancy and to develop an easy-to-use prediction model that uses readily available bedside information to predict the discrepancy and suggest the need for arterial blood gas measurement. This is a prognostic study that used eICU Collaborative Research Database from 2014 to 2015 for model development and MIMIC-IV data from 2008 to 2019 for model validation. To predict the outcome of SpO₂ exceeding SaO₂ by 3% or more, non-invasive, readily available bedside information (patient demographics, vital signs, vasopressor use, ventilator use) was used to develop prediction models with three machine learning methods (decision tree, logistic regression, XGBoost). To make the model accessible, the model was deployed as a web-based application. Additionally, the contribution of each variable was explored using partial dependence plots and SHAP values. From 4,781 admission records in eICU data, a total of 19,804 paired SpO₂ and SaO₂ measurements were used. Among three machine learning models, the XGBoost model demonstrated the best predictive performance with an AUROC of 0.73 and a calibration slope of 0.90. In the validation cohort of MIMIC-IV paired dataset, the performance was AUROC of 0.56. An exploratory model-updating step followed by temporal validation raised performance to AUROC of 0.70 with a calibration slope of 0.85. In both datasets, worse vital signs were associated with the discrepancy (e.g., low blood pressure, low temperature) between SpO₂ and SaO₂. Using non-invasive bedside data, a machine learning model was developed to predict SpO₂–SaO₂ discrepancy and identified vital signs as key contributors. These findings underscore the awareness for hidden hypoxemia and provide the basis of further study to accurately evaluate the actual SaO₂.

Accurate estimation of the ultimate bearing capacity (UBC) of shallow foundations is critical for safe and economical geotechnical design. Traditional approaches depend heavily on extensive and costly field and laboratory investigations, while numerical simulations, though effective, are computationally intensive and time-consuming. To address these limitations, this study investigates the application of machine learning (ML) models for efficient and reliable prediction of the ultimate bearing capacity of shallow foundations. Although numerous studies have explored individual ML techniques for this purpose, a comprehensive and consistent comparison of widely used models under identical conditions remains limited. This research evaluates six ML algorithms; k-Nearest Neighbors (kNN), Artificial Neural Network (NN), Random Forest (RF), Extreme Gradient Boosting (xGBoost), Adaptive Boosting (AdaBoost), and Stochastic Gradient Descent (SGD), using a dataset of 169 experimental results collected from literature. The input features include foundation width (B), depth (D), length-to-width ratio (L/B), soil unit weight (γ), and angle of internal friction (φ). Model performance was assessed using multiple evaluation metrics: coefficient of determination (R²), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE), Mean Squared Error (MSE), and objective function (OBJ). To enhance model interpretability, SHapley Additive Explanations (SHAP) and Partial Dependence Plots (PDPs) were employed to analyze feature importance and input-output relationships, highlighting the influence of both soil properties and foundation geometry on predicted bearing capacity. Among the evaluated models, AdaBoost demonstrated the best overall performance, achieving R² values of 0.939 and 0.881 on the training and testing sets, respectively. Based on the cumulative ranking of the models across all evaluation metrics, the models were ranked in the following order of performance: AdaBoost > kNN > RF > xGBoost > NN > SGD. While the results are promising, a key limitation is the use of single-layer soil data, which restricts applicability to more complex, multilayered soil profiles. Future studies should incorporate multilayer datasets and account for spatial variability to enhance the generalizability and robustness of predictive models.

With the acceleration of urbanization, the coupling relationship between the built environment and urban safety hazards has become increasingly prominent. Irrational spatial structures and resource allocations may aggravate safety hazards and negatively affect residents’ quality of life, thus requiring urgent scientific evaluation and optimization. However, existing studies mostly focus on linear correlation analysis, which makes it difficult to reveal the complex nonlinear mechanisms among multidimensional environmental factors. Taking Cracow (Kraków), Poland as the study area, this research utilizes multi-source spatial data to quantify environmental features such as transportation, socioeconomic conditions, visual landscapes, and public services, in order to uncover their role in the formation of safety hazards. An XGBoost-based safety hazard prediction model is constructed, and SHAP interpretability analysis, together with two-dimensional partial dependence plots (2D PDPs), are introduced to systematically explore the synergistic gains, marginal effects, and resource allocation thresholds of key variables. The results indicate that variables such as average housing price, distance to the nearest police station, and average population density contribute significantly to hazard prediction, and that certain combinations of variables exhibit strong synergistic effects in reducing hazards within medium-range intervals. The study concludes that integrating machine learning with interpretability analysis can not only effectively identify the spatial features associated with high levels of safety hazards, but also provide quantifiable and actionable optimization pathways for urban planning and safety hazard governance. This research further underscores the role of managing urban safety hazards as a key pillar in the sustainable development of cities by linking safety hazard modeling with spatial governance strategies that promote inclusive, resilient, and livable urban environments.

This study employs the uniform design (UD) method to establish a sample database and utilises a machine-learning-based partial dependence plot (PDP) approach to develop a multi-parameter seismic fragility analysis framework for horizontally curved bridge portfolios. Six machine learning (ML) models are compared to identify the optimal seismic fragility prediction model and assess the importance of parameters through permutation importance (PI). Additionally, the PDP is applied to generate seismic fragility curves for the curved bridge portfolios, effectively avoiding the need for high-dimensional mixed integrals. Furthermore, the PDP technique is used to explore the relationship between critical structural attributes and fragility under specified seismic intensity levels. The results indicate that the ML model exhibits favourable fidelity and robustness, with an area under the curve (AUC) exceeding 0.9. The most influential structural attributes affecting the fragility of horizontally curved bridges include boundary type (BT), support design configuration (SPD), column height (H), single-span length (L), and central angle (α). The ductility seismic system and the seismic isolation system for horizontally curved bridges can be preliminarily distinguished based on parameters α, L, and H.

Using machine learning models to predict vaccine hesitancy: a showcase of COVID-19 vaccine hesitancy in rural populations during the pandemic.

IntroductionFrequent droughts and climate fluctuations pose significant challenges to stabilizing and increasing the yields of drought-tolerant crops like sorghum. Accurate, detailed, and spatially explicit yield predictions are essential for precision irrigation, variable fertilization, and food security assessment.MethodsThis study was conducted in the Lifang dryland experimental area in Jinzhong, Shanxi Province, using a sorghum planting experiment. Multispectral imagery and meteorological data were collected simultaneously using a DJI Mavic 3M UAV during key growth stages (seedling emergence, jointing, flowering, and maturity). A “spectral-meteorological-spatial” three-dimensional prediction framework was developed using eight machine learning algorithms. SHAP values and Partial Dependency Plots were used to assess variable importance.ResultsEnsemble learning algorithms performed best, with the Gradient Boosting model achieving an R2 of 0.9491 and Random Forest reaching 0.9070. SHAP analysis revealed that DVI and NDGI were the most important predictors. The jointing stage contributed most to prediction accuracy (R2 = 0.9454), followed by maturity (R² = 0.9215) and flowering (R2 = 0.9075). Yield spatial distribution ranged from 4,291 to 4,965 kg haR-1, with a global Moran’s I index of 0.5552 indicating moderate positive spatial autocorrelation.DiscussionIntegrating UAV multispectral data with machine learning methods enables efficient sorghum yield prediction, with the jointing stage identified as the optimal monitoring period. This study provides crucial technical support for precision planting and efficient sorghum management in arid regions.