Shapley Value Research Articles

Decomposition of intra-household disparity sensitive fuzzy multi-dimensional poverty index: A study of vulnerability through Shapley machine learning

The well accepted multi-dimensional measures have failed to properly project the vulnerability of human-beings towards poverty. Some of the reasons behind this inability may be the failure of the existing measures to consider the graduality within the concept of poverty and the disparities within the household in wealth distribution. So, this work wants to develop a measure to estimate the vulnerability of households in becoming poor through incorporating the intra-household disparities through the factors which suffer from graduality. The decomposition of the grade of vulnerability on the causal factors is also under the purview of this work. To that respect the idea of fuzzy logic and decomposition through artificial intelligence has been used to develop a mathematical framework. So, the idea of Shapley Value Decomposition method has been used extensively. This decomposition is implemented here with the help of Shapley Machine Learning. This decomposition will help the planners to locate the role of different dimensions behind the vulnerability of human beings to become poor more efficiently.

Hybrid game theoretic strategy for optimal relay selection in energy harvesting cognitive radio network

SummaryRelay selection plays a crucial role in enhancing the performance of wireless networks particularly in the context of cognitive radio (CR) systems with energy harvesters. In this paper, we propose a novel approach, namely, CGAPSO Shapley, for the best relay selection while simultaneously optimizing the parameters of signal‐to‐interference‐plus‐noise ratio (SINR), throughput, and outage probability. The CGAPSO Shapley algorithm combines the Shapley value, a cooperative game theory concept, with cellular genetic algorithm particle swarm optimization (CGAPSO) to achieve effective and efficient optimization of relay selection. The CGAPSO framework provides a hybrid structure that integrates cellular genetic algorithm (CGA) and particle swarm optimization (PSO), enabling simultaneous evolution of the population and particles within cells. The incorporation of the Shapley value and the hybrid CGAPSO framework enables effective exploration of the solution space and provides decision‐makers with comprehensive insights for relay selection. By utilizing the Shapley value, we assign weights to the relay nodes based on their contributions to the overall optimization objectives, considering their CR capabilities and energy harvesting capabilities. Some benchmark test functions are used to compare the hybrid algorithm with both the standard CGAPSO, Particle swarm optimization gravitational search algorithm (PSOGSA) and PSO algorithms in evolving best solution. The results show the hybrid algorithm possesses a better capability to escape from local optimums with faster convergence than the standard algorithms. The novel CGAPSO Shapley approach achieves an outage probability of 0.323324, marking a significant improvement of 60% over the outage probability achieved with conventional approach.

Relation between fault characteristic frequencies and local interpretability shapley additive explanations for continuous machine health monitoring

Recently, the Shapley additive explanations models have been extensively studied to enhance explainability of artificial intelligence algorithms, while most of them simply use Shapley additive explanations to rank or measure the importance of different features. In this study, a novel methodology that studies the relation between fault characteristic frequencies and Shapley values generated by local interpretability Shapley additive explanations for machine health monitoring is proposed. Firstly, a simulation model is introduced to generate vibration signals at different health conditions and their spectral amplitudes transformed from Fourier transform are used to investigate the relationship between fault characteristic frequencies and local interpretability Shapley values. It is interestingly found that Shapley values can be used to locate fault characteristic frequencies. Moreover, most of them have negative values in a normal stage and have positive values in an abnormal stage. Based on this finding and Shapley additive explanations, a health indicator construction methodology is proposed to continuously monitor incipient machine faults. Subsequently, an automatic signal filtering method is proposed to remove and eliminate burrs and noise in Shapley values so that fault characteristic frequencies can be clearly revealed by Shapley values for physical fault diagnosis. Two run-to-failure cases are conducted to demonstrate the effectiveness of the proposed methodology and then the superiority of this study is demonstrated by comparing with existing methods for health indicator construction and fault diagnosis, including sparsity parameters, Hjorth parameters, and fast Kurtogram. Comparison results show that the proposed health indicator is more sensitive to the time of incipient fault initiation and interpretable fault diagnosis based on Shapley values has a robust performance. This study first sheds a light on the relationship between fault characteristic frequencies and Shapley values under the scenario of continuous machine health monitoring and seamlessly guides applicants to realize Shapley additive explanations based incipient fault detection and diagnosis.

Recurrent neural network-based prediction of O-GlcNAcylation sites in mammalian proteins

O-GlcNAcylation has the potential to be an important target for therapeutics, but a motif or an algorithm to reliably predict O-GlcNAcylation sites is not available. Current predictive models are insufficient as they fail to generalize, and many are no longer available. This article constructs recurrent neural network models to predict O-GlcNAcylation sites based on protein sequences. Different datasets are evaluated separately and assessed in terms of strengths and issues. Within a given dataset, results are robust to changes in cross-validation and test data as determined by nested validation. The best model achieves an F1 score of 36% (more than 3.5-fold greater than the previous best model) and a Matthews Correlation Coefficient of 35% (more than 4.5-fold greater than the previous best model), and, for the F1 score, 7.6-fold higher than when not using any model. Shapley values are used to interpret the model’s predictions and provide biological insight into O-GlcNAcylation.

Ground-truth validation of uni- and multivariate lesion inference approaches.

Lesion analysis aims to reveal the causal contributions of brain regions to brain functions. Various strategies have been used for such lesion inferences. These approaches can be broadly categorized as univariate or multivariate methods. Here we analysed data from 581 patients with acute ischaemic injury, parcellated into 41 Brodmann areas, and systematically investigated the inferences made by two univariate and two multivariate lesion analysis methods via ground-truth simulations, in which we defined a priori contributions of brain areas to assumed brain function. Particularly, we analysed single-region models, with only single areas presumed to contribute functionally, and multiple-region models, with two contributing regions that interacted in a synergistic, redundant or mutually inhibitory mode. The functional contributions could vary in proportion to the lesion damage or in a binary way. The analyses showed a considerably better performance of the tested multivariate than univariate methods in terms of accuracy and mis-inference error. Specifically, the univariate approaches of Lesion Symptom Mapping as well as Lesion Symptom Correlation mis-inferred substantial contributions from several areas even in the single-region models, and also after accounting for lesion size. By contrast, the multivariate approaches of Multi-Area Pattern Prediction, which is based on machine learning, and Multi-perturbation Shapley value Analysis, based on coalitional game theory, delivered consistently higher accuracy and specificity. Our findings suggest that the tested multivariate approaches produce largely reliable lesion inferences, without requiring lesion size consideration, while the application of the univariate methods may yield substantial mis-localizations that limit the reliability of functional attributions.

Unsupervised Feature Selection to Identify Important ICD-10 and ATC Codes for Machine Learning on a Cohort of Patients With Coronary Heart Disease: Retrospective Study.

The application of machine learning in health care often necessitates the use of hierarchical codes such as the International Classification of Diseases (ICD) and Anatomical Therapeutic Chemical (ATC) systems. These codes classify diseases and medications, respectively, thereby forming extensive data dimensions. Unsupervised feature selection tackles the "curse of dimensionality" and helps to improve the accuracy and performance of supervised learning models by reducing the number of irrelevant or redundant features and avoiding overfitting. Techniques for unsupervised feature selection, such as filter, wrapper, and embedded methods, are implemented to select the most important features with the most intrinsic information. However, they face challenges due to the sheer volume of ICD and ATC codes and the hierarchical structures of these systems. The objective of this study was to compare several unsupervised feature selection methods for ICD and ATC code databases of patients with coronary artery disease in different aspects of performance and complexity and select the best set of features representing these patients. We compared several unsupervised feature selection methods for 2 ICD and 1 ATC code databases of 51,506 patients with coronary artery disease in Alberta, Canada. Specifically, we used the Laplacian score, unsupervised feature selection for multicluster data, autoencoder-inspired unsupervised feature selection, principal feature analysis, and concrete autoencoders with and without ICD or ATC tree weight adjustment to select the 100 best features from over 9000 ICD and 2000 ATC codes. We assessed the selected features based on their ability to reconstruct the initial feature space and predict 90-day mortality following discharge. We also compared the complexity of the selected features by mean code level in the ICD or ATC tree and the interpretability of the features in the mortality prediction task using Shapley analysis. In feature space reconstruction and mortality prediction, the concrete autoencoder-based methods outperformed other techniques. Particularly, a weight-adjusted concrete autoencoder variant demonstrated improved reconstruction accuracy and significant predictive performance enhancement, confirmed by DeLong and McNemar tests (P<.05). Concrete autoencoders preferred more general codes, and they consistently reconstructed all features accurately. Additionally, features selected by weight-adjusted concrete autoencoders yielded higher Shapley values in mortality prediction than most alternatives. This study scrutinized 5 feature selection methods in ICD and ATC code data sets in an unsupervised context. Our findings underscore the superiority of the concrete autoencoder method in selecting salient features that represent the entire data set, offering a potential asset for subsequent machine learning research. We also present a novel weight adjustment approach for the concrete autoencoders specifically tailored for ICD and ATC code data sets to enhance the generalizability and interpretability of the selected features.

Energy Consumption Outlier Detection with AI Models in Modern Cities: A Case Study from North-Eastern Mexico

The development of smart cities will require the construction of smart buildings. Smart buildings will demand the incorporation of elements for efficient monitoring and control of electrical consumption. The development of efficient AI algorithms is needed to generate more accurate electricity consumption predictions; therefore; anomaly detection in electricity consumption predictions has become an important research topic. This work focuses on the study of the detection of anomalies in domestic electrical consumption in Mexico. A predictive machine learning model of future electricity consumption was generated to evaluate various anomaly-detection techniques. Their effectiveness in identifying outliers was determined, and their performance was documented. A 30-day forecast of electrical consumption and an anomaly-detection model have been developed using isolation forest. Isolation forest successfully captured up to 75% of the anomalies. Finally, the Shapley values have been used to generate an explanation of the results of a model capable of detecting anomalous data for the Mexican context.

Strength Prediction in UHPC with XGBoost Model and Shapley Algorithm Interpretation

This study employs the XGBoost regression model to predict the strength of UHPC and utilizes the Shapley algorithm to interpret the model's predictions, revealing the impact of various feature parameters. The results demonstrate that the XGBoost regression model effectively fits the data and possesses strong predictive capabilities. Furthermore, the interaction between silica fume and cement significantly influences the model predictions. Additionally, using tools such as the Shapley heatmap, the study analyzes the model's characteristics and finds that only a subset of samples have Shapley values below the mean, indicating the dataset contains relatively few high-quality samples. Through the Shapley algorithm, the optimal range for silica fume quantity is determined to be between 0 and 320 kg. This research validates the effectiveness of the XGBoost regression model for predicting UHPC strength and enhances model interpretability using the Shapley algorithm.

Associated Probabilities’ Aggregations in Fuzzy Collaborative Filtering Recommender System Prediction

AbstractIn this article, the expert evaluations transformed in the multi-attribute decision-making (MADM) model are presented in the discrimination q-rung picture linguistic fuzzy numbers (q-RPLFNs). In the construction of a second-order additive fuzzy measure (TOAFM) the attributes’ interaction indexes and Shapley values are taken into account. The Shapley entropy maximum principle for identification of associated probabilities class (APC) of a TOAFM is constructed. Based on the APC of the TOAFM, a new aggregation operators’ class is constructed which represents some hybrid extensions of ordered weighted averaging (OWA), geometric (OWG), the Choquet integral averaging (CA) and geometric (CG) operators under discrimination q-rung orthopair fuzzy (q-ROF) and q-rung picture linguistic fuzzy (q-RPLF) information. These operators, constructed for the q-RPLF and q-ROF environments, take into account the overall pair interactions among attributes. Main properties on the correctness of extensions are proved: for the lower and upper capacities of order 2, all constructed operators consequently coincide with q-ROF and q-RPLF Choquet averaging and geometric operators, respectively. Constructed operators in the evaluation of prediction of fuzzy Collaborative Filtering Recommender Systems (CFRS) are used. New symmetric discrimination measures as some extensions of discrimination measures for the fuzzy CFRS are proposed. Users’ profile data by the constructed operators in the new similarity measure under q-rung picture linguistic environment are aggregated. The developed new approach is schematically described in such a way that it can be “embedded” in any existing CFRS model. An example is given to illustrate the results, for which the software designed to aggregate profile data for similarity comparison provides the use of new and well-known classical aggregation operators.

Machine learning models with distinct Shapley value explanations decouple feature attribution and interpretation for chemical compound predictions

Machine learning models with distinct Shapley value explanations decouple feature attribution and interpretation for chemical compound predictions

Machine Learning Predicts Unplanned Care Escalations for Post-Anesthesia Care Unit Patients during the Perioperative Period: A Single-Center Retrospective Study

Background: Despite low mortality for elective procedures in the United States and developed countries, some patients have unexpected care escalations (UCE) following post-anesthesia care unit (PACU) discharge. Studies indicate patient risk factors for UCE, but determining which factors are most important is unclear. Machine learning (ML) can predict clinical events. We hypothesized that ML could predict patient UCE after PACU discharge in surgical patients and identify specific risk factors. Methods: We conducted a single center, retrospective analysis of all patients undergoing non-cardiac surgery (elective and emergent). We collected data from pre-operative visits, intra-operative records, PACU admissions, and the rate of UCE. We trained a ML model with this data and tested the model on an independent data set to determine its efficacy. Finally, we evaluated the individual patient and clinical factors most likely to predict UCE risk. Results: Our study revealed that ML could predict UCE risk which was approximately 5% in both the training and testing groups. We were able to identify patient risk factors such as patient vital signs, emergent procedure, ASA Status, and non-surgical anesthesia time as significant variable. We plotted Shapley values for significant variables for each patient to help determine which of these variables had the greatest effect on UCE risk. Of note, the UCE risk factors identified frequently by ML were in alignment with anesthesiologist clinical practice and the current literature. Conclusions: We used ML to analyze data from a single-center, retrospective cohort of non-cardiac surgical patients, some of whom had an UCE. ML assigned risk prediction for patients to have UCE and determined perioperative factors associated with increased risk. We advocate to use ML to augment anesthesiologist clinical decision-making, help decide proper disposition from the PACU, and ensure the safest possible care of our patients.

A multi-ship power sharing strategy: Using two-stage robust optimization and Shapley value approach

In recent years, the use of cold ironing (CI) has effectively reduced the carbon emissions of ships in port areas. However, due to the limitation of port CI quantity and power supply capacity, the power demand of some ships cannot be met. To solve this problem, this paper proposes a multi-ship power sharing strategy based on two-stage robust optimization and improved Shapley value method. Firstly, considering the uncertainty of ship photovoltaic power generation, a multi-ship power sharing model based on two-stage robust optimization is established. This model is a three-level optimization model with mixed integer variables, which is a NP-hard problem. In this paper, the nested column-and-constraint generation algorithm combined with duality theory and big-M method is used to obtain the optimal scheduling strategy of ship shared power, CI power and load demand response power. Secondly, an improved Shapley value method considering berth and remaining berthing time is proposed to realize the cost allocation in the process of ship power sharing. Finally, the effectiveness of the multi-ship power sharing strategy in reducing berthing costs and carbon emissions is verified by simulation. This method is expected to provide a new idea for the development of green ports.

Understanding shoppers’ cross-channel analysis of influencing factors of online and offline channels: Evidence from clothing product

As the online to offline (O2O) retail market develops rapidly, most consumers become O2O shoppers who shop online and offline. However, researchers seldom focus on O2O retailers collaborating online and offline channels to better satisfy consumers' needs. To fill the gap, this study explores the neglected problem from the shoppers’ cross-channel analysis perspective. In this paper, we used text data mining to capture shoppers' online comments on Suning.com, where we selected T-shirts, skirts and trousers as products to be analyzed. After determining the influencing factors, we used social network analysis to construct the two relation networks based on the semantic set of shoppers' comments. This study reveals the relations between the influencing factors of online and offline channels and finds shoppers' cross-channel analysis behavior characteristics by analyzing the density and centrality indicators of the rebuilt relation network. The research results demonstrate that the impacts of the influencing factors on shoppers' purchase intentions are different. Offline product experience, online product comments, online product price, and offline product price significantly influence and control their purchase intention more than the other factors when shoppers cross-channel analyze the influencing factors. Moreover, this study uses the Shapley model to quantitatively analyze the impact of influencing factors on shoppers' purchase intention by building collaborative alliances. The Shapley values confirm that shoppers attach the highest importance to offline product experience, followed by online product comments, online product price and so on. The findings can improve O2O retailers' collaborative marketing strategies.

Variable importance analysis of wind turbine extreme responses with Shapley value explanation

As a leading form of renewable energy, wind power is gaining prominence with its decreasing levelized cost of electricity. The wind turbine extreme analysis is crucial for the structural reliability and integrity of wind turbines. Variable importance analysis provides a quantitative assessment of how significantly each variable influences model predictions. Variance-based importance measure quantifies each input variable’s contribution to the overall variance of a model or system. Such analyses are critical for interpreting the model and selecting features, thereby facilitating informed decision-making. This study uses Shapley value explanations to conduct a variable importance analysis of three wind turbine extreme responses, blade tip-tower clearance, blade root bending moment, and tower base bending moment. Random forest-based regression models and an improved Shapley effect evaluation algorithm are employed to improve the efficiency of the numerical analysis. The findings reveal the relative importance of five inputs, two wind parameters, one aerodynamic parameter, and two structural parameters, on each wind turbine extreme response variable. Additionally, the study explores how different dependency structures and varying correlation coefficients, even within the same correlation structure, affect the outcomes of variable importance analysis.

At-admission prediction of mortality and pulmonary embolism in an international cohort of hospitalised patients with COVID-19 using statistical and machine learning methods

By September 2022, more than 600 million cases of SARS-CoV-2 infection have been reported globally, resulting in over 6.5 million deaths. COVID-19 mortality risk estimators are often, however, developed with small unrepresentative samples and with methodological limitations. It is highly important to develop predictive tools for pulmonary embolism (PE) in COVID-19 patients as one of the most severe preventable complications of COVID-19. Early recognition can help provide life-saving targeted anti-coagulation therapy right at admission. Using a dataset of more than 800,000 COVID-19 patients from an international cohort, we propose a cost-sensitive gradient-boosted machine learning model that predicts occurrence of PE and death at admission. Logistic regression, Cox proportional hazards models, and Shapley values were used to identify key predictors for PE and death. Our prediction model had a test AUROC of 75.9% and 74.2%, and sensitivities of 67.5% and 72.7% for PE and all-cause mortality respectively on a highly diverse and held-out test set. The PE prediction model was also evaluated on patients in UK and Spain separately with test results of 74.5% AUROC, 63.5% sensitivity and 78.9% AUROC, 95.7% sensitivity. Age, sex, region of admission, comorbidities (chronic cardiac and pulmonary disease, dementia, diabetes, hypertension, cancer, obesity, smoking), and symptoms (any, confusion, chest pain, fatigue, headache, fever, muscle or joint pain, shortness of breath) were the most important clinical predictors at admission. Age, overall presence of symptoms, shortness of breath, and hypertension were found to be key predictors for PE using our extreme gradient boosted model. This analysis based on the, until now, largest global dataset for this set of problems can inform hospital prioritisation policy and guide long term clinical research and decision-making for COVID-19 patients globally. Our machine learning model developed from an international cohort can serve to better regulate hospital risk prioritisation of at-risk patients.

Cooperative supply game and its revenue allocation method considering location of transportation hub

PurposeThis paper aims to study the establishment of cooperative supply game model considering transportation hub location, and design the profit allocation rule of the cooperative supply coalition.Design/methodology/approachBased on the economic lost-sizing (ELS) game model and considering the location of transportation hub and the topology design of basic traffic network, we build a supply game model to maximize the profit of cooperative supply coalition. Based on the principle of proportion and the method of process allocation, we suppose the procedural proportional solution of the supplier cooperative supply game.FindingsThrough numerical examples, the validity and applicability of the proposed model and the procedural proportional solution were verified by comparing the procedural proportional solution with the weighted Shapley value, the equal division solution and the proportional rule.Originality/valueThis paper constructs a feasible mixed integer programming model for cooperative supply game. We also provide the algorithm of the allocation rule of cooperative supply game and the property analysis of the allocation rule.

Shapley-based graph explanation in embedding space

Graph Neural Networks (GNNs) have recently achieved remarkable success in learning graph structures and have been applied in a variety of practical applications such as medical diagnosis, drug discovery, chemical compound synthesis, and traffic forecasting. However, like other deep learning methods, GNNs are black-box networks with inexplicable results, restricting the applicability of GNNs in many important applications such as biochemistry and medicine. This paper focuses on the field of explaining graph learning methods, which is still less explored and lacks strong theoretical grounds. Based on Shapley value from game theory, we propose a novel graph explainer, named Shapley and Embedding-based Graph Explainer (SEGE), which builds a linear approximator in node embedding space to interpret the GNNs’ prediction of an input graph. Experiments on synthetic and real-world datasets demonstrate that SEGE achieves state-of-the-art performance and is significantly better than baseline models both qualitatively and quantitatively. Moreover, SEGE owns the capacity of automorphic equivalence preservation, which is not observed in existing explainers.

Random partitions, potential, value, and externalities

The Shapley value equals a player's contribution to the potential of a game. The potential is a most natural one-number summary of a game, which can be computed as the expected accumulated worth of a random partition of the players. This computation integrates the coalition formation of all players and readily extends to games with externalities. We investigate those potential functions for games with externalities that can be computed this way. It turns out that the potential that corresponds to the MPW solution introduced by Macho-Stadler et al. (2007, J. Econ. Theory 135, 339–356) is unique in the following sense. It is obtained as the expected accumulated worth of a random partition, it generalizes the potential for games without externalities, and it induces a solution that satisfies the null player property even in the presence of externalities.

A decision framework for improving the service quality of charging stations based on online reviews and evolutionary game theory

With “charging anxiety” gradually replacing “range anxiety” as the major obstacle for consumers to purchase electric vehicles (EVs), the quantity-driven rather than quality-driven charging station development model barely meets the development of the EV market. It is of great practical significance that a comprehensive and in-depth insight into charging stations’ customer requirements (CRs) to uncover their pain points and improvement measures. Therefore, this study develops a decision framework for improving EV charging service quality based on quality function deployment (QFD). First, CRs are extracted based on charging station online reviews and classified by the revised importance performance analysis (IPA) method to identify the charging service’s main highlights and pain points. Then, the process of achieving consensus among experts on evaluating the correlation between CRs and service design requirements (DRs) is considered as an evolutionary game of coalition, with a meritocratic Fermi rule considering affinities (MFA) being introduced. Finally, the importance of DRs is determined by combining the Shapley value and risk aversion theory. The results indicate that regulation and convenience are the main highlights of charging stations to satisfy EV users, while reliability and assurance are primary pain points. The charging station operators should prioritize their limited resources on providing efficient customer and maintenance services, installing charging stations with international standards, and regularly inspecting and updating charging infrastructures. This study is beneficial for charging station operators to understand what customers want and how to satisfy them.

Deep survival analysis for interpretable time-varying prediction of preeclampsia risk

ObjectiveSurvival analysis is widely utilized in healthcare to predict the timing of disease onset. Traditional methods of survival analysis are usually based on Cox Proportional Hazards model and assume proportional risk for all subjects. However, this assumption is rarely true for most diseases, as the underlying factors have complex, non-linear, and time-varying relationships. This concern is especially relevant for pregnancy, where the risk for pregnancy-related complications, such as preeclampsia, varies across gestation. Recently, deep learning survival models have shown promise in addressing the limitations of classical models, as the novel models allow for non-proportional risk handling, capturing nonlinear relationships, and navigating complex temporal dynamics. MethodsWe present a methodology to model the temporal risk of preeclampsia during pregnancy and investigate the associated clinical risk factors. We utilized a retrospective dataset including 66,425 pregnant individuals who delivered in two tertiary care centers from 2015 to 2023. We modeled the preeclampsia risk by modifying DeepHit, a deep survival model, which leverages neural network architecture to capture time-varying relationships between covariates in pregnancy. We applied time series k-means clustering to DeepHit’s normalized output and investigated interpretability using Shapley values. ResultsWe demonstrate that DeepHit can effectively handle high-dimensional data and evolving risk hazards over time with performance similar to the Cox Proportional Hazards model, achieving an area under the curve (AUC) of 0.78 for both models. The deep survival model outperformed traditional methodology by identifying time-varied risk trajectories for preeclampsia, providing insights for early and individualized intervention. K-means clustering resulted in patients delineating into low-risk, early-onset, and late-onset preeclampsia groups—notably, each of those has distinct risk factors. ConclusionThis work demonstrates a novel application of deep survival analysis in time-varying prediction of preeclampsia risk. Our results highlight the advantage of deep survival models compared to Cox Proportional Hazards models in providing personalized risk trajectory and demonstrating the potential of deep survival models to generate interpretable and meaningful clinical applications in medicine.