Phylogenetic Diversity Indices from an Affine and Projective Viewpoint.

Phylogenetic diversity indices are commonly used to rank the elements in a collection of species or populations for conservation purposes. The derivation of these indices is typically based on some quantitative description of the evolutionary history of the species in question, which is often given in terms of a phylogenetic tree. Both rooted and unrooted phylogenetic trees can be employed, and there are close connections between the indices that are derived in these two different ways. In this paper, we introduce more general phylogenetic diversity indices that can be derived from collections of subsets (clusters) and collections of bipartitions (splits) of the given set of species. Such indices could be useful, for example, in case there is some uncertainty in the topology of the tree being used to derive a phylogenetic diversity index. As well as characterizing some of the indices that we introduce in terms of their special properties, we provide a link between cluster-based and split-based phylogenetic diversity indices that uses a discrete analogue of the classical link between affine and projective geometry. This provides a unified framework for many of the various phylogenetic diversity indices used in the literature based on rooted and unrooted phylogenetic trees, generalizations and new proofs for previous results concerning tree-based indices, and a way to define some new phylogenetic diversity indices that naturally arise as affine or projective variants of each other or as generalizations of tree-based indices.

Optimizing Collaborative Crowdsensing: A Graph Theoretical Approach to Team Recruitment and Fair Incentive Distribution.

Collaborative crowdsensing is a team collaboration model that harnesses the intelligence of a large network of participants, primarily applied in areas such as intelligent computing, federated learning, and blockchain. Unlike traditional crowdsensing, user recruitment in collaborative crowdsensing not only considers the individual capabilities of users but also emphasizes their collaborative abilities. In this context, this paper takes a unique approach by modeling user interactions as a graph, transforming the recruitment challenge into a graph theory problem. The methodology employs an enhanced Prim algorithm to identify optimal team members by finding the maximum spanning tree within the user interaction graph. After the recruitment, the collaborative crowdsensing explored in this paper presents a challenge of unfair incentives due to users engaging in free-riding behavior. To address these challenges, the paper introduces the MR-SVIM mechanism. Initially, the process begins with a Gaussian mixture model predicting the quality of users' tasks, combined with historical reputation values to calculate their direct reputation. Subsequently, to assess users' significance within the team, aggregation functions and the improved PageRank algorithm are employed for local and global influence evaluation, respectively. Indirect reputation is determined based on users' importance and similarity with interacting peers. Considering the comprehensive reputation value derived from the combined assessment of direct and indirect reputations, and integrating the collaborative capabilities among users, we have formulated a feature function for contribution. This function is applied within an enhanced Shapley value method to assess the relative contributions of each user, achieving a more equitable distribution of earnings. Finally, experiments conducted on real datasets validate the fairness of this mechanism.

Efficiency evaluation of low impact development practices on urban flood risk.

Urban flood risk assessment delivers invaluable information regarding flood management as well as preventing the associated risks in urban areas. The present study prepares a flood risk map and evaluate the practices of low-impact development (LID) intended to decrease the flood risk in Shiraz Municipal District 4, Fars province, Iran. So, this study investigate flood vulnerability using MCDM models and some indices, including population density, building age, socio-economic conditions, floor area ratio, literacy, the elderly population, and the number of building floors to. Then, the map of thematic layers affecting the urban flood hazard, including annual mean rainfall, land use, elevation, slope percentage, curve number, distance from channel, depth of groundwater, and channel density, was prepared in GIS. After conducting a multicollinearity test, data mining models were used to create the urban flood hazard map, and the urban flood risk map was produced using ArcGIS 10.8. The evaluation of vulnerability models was shown through the use of Boolean logic that TOPSIS and VIKOR models were effective in identifying urban flooding vulnerable areas. Data mining models were also evaluated using ROC and precision-recall curves, indicating the accuracy of the RF model. The importance of input variables was measured using Shapley value, which showed that curve number, land use, and elevation were more important in flood hazard modeling. According to the results, 37.8 percent of the area falls into high and very high categories in terms of flooding risk. The study used a stormwater management model (SWMM) to simulate node flooding and provide management scenarios for rainfall events with a return period ranging from 2 to 50 years and five rainstorm events. The use of LID practices in flood management was found to be effective for rainfall events with a return period of less than 10 years, particularly for two-year events. However, the effectiveness of LID practices decreases with an increase in the return period. By applying a combined approach to a region covering approximately 10 percent of the total area of Shiraz Municipal District 4, a reduction of 2-22.8 percent in node flooding was achieved. The analysis of data mining and MCDM models with a physical model revealed that more than 60% of flooded nodes were classified as "high" and "very high" risk categories in the RF-VIKOR and RF-TOPSIS risk models.

Model parameter estimation with imprecise information.

Model parameter estimation is a well-known inverse problem, as long as single-value point data are available as observations of system performance measurement. However, classical statistical methods, such as the minimization of an objective function or maximum likelihood, are no longer straightforward, when measurements are imprecise in nature. Typical examples of the latter include censored data and binary information. Here, we explore Approximate Bayesian Computation as a simple method to perform model parameter estimation with such imprecise information. We demonstrate the method for the example of a plain rainfall-runoff model and illustrate the advantages and shortcomings. Last, we outline the value of Shapley values to determine which type of observation contributes to the parameter estimation and which are of minor importance.

Use of multi-perturbation Shapley analysis in lesion studies of functional networks: The case of upper limb paresis.

Understanding the impact of variation in lesion topography on the expression of functional impairments following stroke is important, as it may pave the way to modeling structure-function relations in statistical terms while pointing to constraints for adaptive remapping and functional recovery. Multi-perturbation Shapley-value analysis (MSA) is a relatively novel game-theoretical approach for multivariate lesion-symptom mapping. In this methodological paper, we provide a comprehensive explanation of MSA. We use synthetic data to assess the method's accuracy and perform parameter optimization. We then demonstrate its application using a cohort of 107 first-event subacute stroke patients, assessed for upper limb (UL) motor impairment (Fugl-Meyer Assessment scale). Under the conditions tested, MSA could correctly detect simulated ground-truth lesion-symptom relationships with a sensitivity of 75% and specificity of ~90%. For real behavioral data, MSA disclosed a strong hemispheric effect in the relative contribution of specific regions-of-interest (ROIs): poststroke UL motor function was mostly contributed by damage to ROIs associated with movement planning (supplementary motor cortex and superior frontal gyrus) following left-hemispheric damage (LHD) and by ROIs associated with movement execution (primary motor and somatosensory cortices and the ventral brainstem) following right-hemispheric damage (RHD). Residual UL motor ability following LHD was found to depend on a wider array of brain structures compared to the residual motor ability of RHD patients. The results demonstrate that MSA can provide a unique insight into the relative importance of different hubs in neural networks, which is difficult to obtain using standard univariate methods.

WindowSHAP: An efficient framework for explaining time-series classifiers based on Shapley values.

Unpacking and comprehending how black-box machine learning algorithms (such as deep learning models) make decisions has been a persistent challenge for researchers and end-users. Explaining time-series predictive models is useful for clinical applications with high stakes to understand the behavior of prediction models, e.g., to determine how different variables and time points influence the clinical outcome. However, existing approaches to explain such models are frequently unique to architectures and data where the features do not have a time-varying component. In this paper, we introduce WindowSHAP, a model-agnostic framework for explaining time-series classifiers using Shapley values. We intend for WindowSHAP to mitigate the computational complexity of calculating Shapley values for long time-series data as well as improve the quality of explanations. WindowSHAP is based on partitioning a sequence into time windows. Under this framework, we present three distinct algorithms of Stationary, Sliding and Dynamic WindowSHAP, each evaluated against baseline approaches, KernelSHAP and TimeSHAP, using perturbation and sequence analyses metrics. We applied our framework to clinical time-series data from both a specialized clinical domain (Traumatic Brain Injury - TBI) as well as a broad clinical domain (critical care medicine). The experimental results demonstrate that, based on the two quantitative metrics, our framework is superior at explaining clinical time-series classifiers, while also reducing the complexity of computations. We show that for time-series data with 120 time steps (hours), merging 10 adjacent time points can reduce the CPU time of WindowSHAP by 80 % compared to KernelSHAP. We also show that our Dynamic WindowSHAP algorithm focuses more on the most important time steps and provides more understandable explanations. As a result, WindowSHAP not only accelerates the calculation of Shapley values for time-series data, but also delivers more understandable explanations with higher quality.

A study on the factors influencing the utilization of public health services by China's migrant population based on the Shapley value method.

BACKGROUND: The health of migrants has received significant global attention, and it is a particularly significant concern in China, which has the largest migrant population in the world. Analyzing data on samples from the Chinese population holds practical significance. For instance, one can delve into an in-depth analysis of the factors impacting (1) the health records of residents in distinct regions and (2) the current state of family doctor contracts. This study explores the barriers to access these two health services and the variations in the effects and contribution magnitudes. METHODS: This study involved data from 138,755 individuals, extracted from the 2018 National Migration Population Health and Family Planning Dynamic Monitoring Survey database. The theoretical framework employed was the Anderson health service model. To investigate the features and determinants of basic public health service utilization among the migrant population across different regions of China, including the influence of enabling resources and demand factors, x2 tests and binary logistic regression analyses were conducted. The Shapley value method was employed to assess the extent of influence of each factor. RESULTS: The utilization of various service types varied among the migrant population, with significant regional disparities. The results of the decomposition of the Shapley value method highlighted variations in the mechanism underlying the influence of propensity characteristics, enabling resources, and demand factors between the two health service types. Propensity characteristics and demand factors were found to be the primary dimensions with the highest explanatory power; among them, health education for chronic disease prevention and treatment was the most influential factor. CONCLUSION: To better meet the health needs of the migrant population, regional barriers need to be broken down, and the relevance and effectiveness of publicity and education need to be improved. Additionally, by considering the education level, demographic characteristics, and mobility characteristics of the migrant population, along with the relevant health policies, the migrant population needs to be guided to maintain the health records of residents. They should also be encouraged to sign a contract with a family doctor in a more effective manner to promote the equalization of basic health services for the migrant population.

A regional cooperative reduction game model for air pollution control in North China.

Due to variations in economic scale, economic structure, and technological advancement across different Chinese provinces and cities, the cost of air pollution reduction differs significantly. Therefore, the total reduction cost can be decreased by capitalizing on these regional discrepancies in reduction cost to carry out cooperative emission reduction. In this paper, taking NOx reduction in North China as an example, a regional cooperative reduction game (CRG) model was constructed to minimize the total cost of emission reduction while achieving future emission reduction targets. The fair allocation of benefits from cooperation plays a crucial role in motivating regions to participate into the cooperation. A comprehensive mechanism of benefits allocation was proposed to achieve fair transferred compensation. The mechanism combines the consumption responsibility principle based on input-output theory and the Shapley value method based on game theory. Compared to the cost before the optimized collaboration, the CRG model will save 20.36% and 13.71% of the total reduction cost in North China, respectively, under the target of 17.68% NOx reduction by 2025 and 66.44% NOx reduction by 2035 relative to 2020. This method can be employed in other regions to achieve targets for air pollution reduction at minimum cost, and to motivate inter-regional cooperation with this practical and fair way of transferred compensation.

The evolutionary trends of health inequality among elderly Chinese people and influencing factors of these trends from 2005 to 2017.

Reducing health inequality and ensuring national health equity have become issues of great concern to all countries in the world. This paper based on the ordered Probit model and concentrated index decomposition method, analysed the influencing factors and evolution trend of health inequality among the elderly with high age in China from 2005 to 2017. The study found that in 2005-2017, the self-rated health distribution of the elderly with high age in China showed an obvious inverted "U" shape, with the proportion of general and relatively healthy being the largest, while the proportion of unhealthy and very healthy was lower. Lifestyle, family income, and age were the main important factors to expand health inequality. Therefore, encouraging the elderly with high age to develop good living habits and narrowing the income gap of the elderly are conducive to solving the health inequality of the elderly with high age and achieving the goals of active ageing and healthy ageing.

Zero-Day Malware Detection and Effective Malware Analysis Using Shapley Ensemble Boosting and Bagging Approach.

Software products from all vendors have vulnerabilities that can cause a security concern. Malware is used as a prime exploitation tool to exploit these vulnerabilities. Machine learning (ML) methods are efficient in detecting malware and are state-of-art. The effectiveness of ML models can be augmented by reducing false negatives and false positives. In this paper, the performance of bagging and boosting machine learning models is enhanced by reducing misclassification. Shapley values of features are a true representation of the amount of contribution of features and help detect top features for any prediction by the ML model. Shapley values are transformed to probability scale to correlate with a prediction value of ML model and to detect top features for any prediction by a trained ML model. The trend of top features derived from false negative and false positive predictions by a trained ML model can be used for making inductive rules. In this work, the best performing ML model in bagging and boosting is determined by the accuracy and confusion matrix on three malware datasets from three different periods. The best performing ML model is used to make effective inductive rules using waterfall plots based on the probability scale of features. This work helps improve cyber security scenarios by effective detection of false-negative zero-day malware.

Assessment of the influence of features on a classification problem: An application to COVID-19 patients.

This paper deals with an important subject in classification problems addressed by machine learning techniques: the evaluation of the influence of each of the features on the classification of individuals. Specifically, a measure of that influence is introduced using the Shapley value of cooperative games. In addition, an axiomatic characterisation of the proposed measure is provided based on properties of efficiency and balanced contributions. Furthermore, some experiments have been designed in order to validate the appropriate performance of such measure. Finally, the methodology introduced is applied to a sample of COVID-19 patients to study the influence of certain demographic or risk factors on various events of interest related to the evolution of the disease.

Best variable identification by means of data-mining and cooperative game theory.

OBJECTIVE: To develop and evaluate methods to assess single and grouped variables impact on measuring intervention severities and support a search for most expressive variables. METHODS: Datasets of cohort studies are analyzed automatically based on algorithms. For this, a metric is developed to compare measured variables in different cohorts in a data-mining process. Variables are measured in all possible combinations to detect possible synergies of certain variable constellations and allow for a ranking of the combinations' expressiveness. Such ranking serves as a basis for a wide range of algorithmic data analysis. In an exemplary application, every group member's impact on the total result is determined based on the principle of the cooperative game theory besides to the total expressiveness of the variable groups. RESULTS: For different types of interventions, the method is applied to experimental data containing multiple recorded medical lab values. The expressiveness of variable combinations to indicate severity is ranked by means of a metric. Within each combination, any variable's contribution to the total effect is determined and accumulated over whole datasets to yield local and global variable importance measures. The computed results have been successfully matched with clinical expectations to prove their plausibility. CONCLUSION: Algorithmic evaluation shows to be a promising approach in automatized quantification of variable expressiveness. It can assess descriptive power of measurements, help to improve future study designs and expose worthwhile research issues.

A game theory approach for risk analysis and security force deployment against multiple coordinated attacks.

The proposed model determines the allocation of security forces in response to terrorist events with a series of coordinated attacks such as the Paris terror attacks in 2015. Two games are constructed, representing the two stages needed for the rapid deployment of security forces. The first stage applies a firearms assault game to analyze the interaction behaviors between the response agent (or security force commander) and the attackers in each response district. The terrorist threat value (TV) during a firearms assault event can then be derived from the mixed strategy Nash equilibrium. The TVs are input to the second stage for computing the Shapley value for each event, in terms of the majority of TVs of all firearms assaults. The Shapley values are then used to create a set for reallocation of the limited security forces to respond to the multiple firearms assaults. The experimental results show the proposed division to fairer than the proportional division for allocating security forces.

Mathematical indices for the influence of risk factors on the lethality of a disease.

We develop a theoretical model to measure the relative relevance of different pathologies of the lethality of a disease in society. This approach allows a ranking of diseases to be determined, which can assist in establishing priorities for vaccination campaigns or prevention strategies. Among all possible measurements, we identify three families of rules that satisfy a combination of relevant properties: neutrality, irrelevance, and one of three composition concepts. One of these families includes, for instance, the Shapley value of the associated cooperative game. The other two families also include simple and intuitive indices. As an illustration, we measure the relative relevance of several pathologies in lethality due to COVID-19.

Shapley-Based Estimation of Company Value-Concept, Algorithms and Parameters.

The aim of the article is to propose a new method of valuation of a company, considering its ownership relations with other companies. For this purpose, the concept of the Shapley value from cooperative game theory is used as the basis for assessing such dependent companies. The paper presents proposals for Shapley value calculation algorithms for our model. We expand our model by discussing personal relations in addition to ownership relations and point out how intuitionistic fuzzy sets may be helpful in this context. As a result, we propose two new expanded models. In the first probabilistic model, we apply Pearson's correlation coefficient, in the second, we use a correlation coefficient between intuitionistic fuzzy sets to determine the personal relationships. Finally, we present and interpret results for a real-world economic network with 17 companies.

A Multi-Objective Multi-Label Feature Selection Algorithm Based on Shapley Value.

Multi-label learning is dedicated to learning functions so that each sample is labeled with a true label set. With the increase of data knowledge, the feature dimensionality is increasing. However, high-dimensional information may contain noisy data, making the process of multi-label learning difficult. Feature selection is a technical approach that can effectively reduce the data dimension. In the study of feature selection, the multi-objective optimization algorithm has shown an excellent global optimization performance. The Pareto relationship can handle contradictory objectives in the multi-objective problem well. Therefore, a Shapley value-fused feature selection algorithm for multi-label learning (SHAPFS-ML) is proposed. The method takes multi-label criteria as the optimization objectives and the proposed crossover and mutation operators based on Shapley value are conducive to identifying relevant, redundant and irrelevant features. The comparison of experimental results on real-world datasets reveals that SHAPFS-ML is an effective feature selection method for multi-label classification, which can reduce the classification algorithm's computational complexity and improve the classification accuracy.

Game theoretic centrality: a novel approach to prioritize disease candidate genes by combining biological networks with the Shapley value.

BACKGROUND: Complex human health conditions with etiological heterogeneity like Autism Spectrum Disorder (ASD) often pose a challenge for traditional genome-wide association study approaches in defining a clear genotype to phenotype model. Coalitional game theory (CGT) is an exciting method that can consider the combinatorial effect of groups of variants working in concert to produce a phenotype. CGT has been applied to associate likely-gene-disrupting variants encoded from whole genome sequence data to ASD; however, this previous approach cannot take into account for prior biological knowledge. Here we extend CGT to incorporate a priori knowledge from biological networks through a game theoretic centrality measure based on Shapley value to rank genes by their relevance-the individual gene's synergistic influence in a gene-to-gene interaction network. Game theoretic centrality extends the notion of Shapley value to the evaluation of a gene's contribution to the overall connectivity of its corresponding node in a biological network. RESULTS: We implemented and applied game theoretic centrality to rank genes on whole genomes from 756 multiplex autism families. Top ranking genes with the highest game theoretic centrality in both the weighted and unweighted approaches were enriched for pathways previously associated with autism, including pathways of the immune system. Four of the selected genes HLA-A, HLA-B, HLA-G, and HLA-DRB1-have also been implicated in ASD and further support the link between ASD and the human leukocyte antigen complex. CONCLUSIONS: Game theoretic centrality can prioritize influential, disease-associated genes within biological networks, and assist in the decoding of polygenic associations to complex disorders like autism.

Game theoretical mapping of white matter contributions to visuospatial attention in stroke patients with hemineglect.

White matter bundles linking gray matter nodes are key anatomical players to fully characterize associations between brain systems and cognitive functions. Here we used a multivariate lesion inference approach grounded in coalitional game theory (multiperturbation Shapley value analysis, MSA) to infer causal contributions of white matter bundles to visuospatial orienting of attention. Our work is based on the characterization of the lesion patterns of 25 right hemisphere stroke patients and the causal analysis of their impact on three neuropsychological tasks: line bisection, letter cancellation, and bells cancellation. We report that, out of the 11 white matter bundles included in our MSA coalitions, the optic radiations, the inferior fronto-occipital fasciculus and the anterior cingulum were the only tracts to display task-invariant contributions (positive, positive, and negative, respectively) to the tasks. We also report task-dependent influences for the branches of the superior longitudinal fasciculus and the posterior cingulum. By extending prior findings to white matter tracts linking key gray matter nodes, we further characterize from a network perspective the anatomical basis of visual and attentional orienting processes. The knowledge about interactions patterns mediated by white matter tracts linking cortical nodes of attention orienting networks, consolidated by further studies, may help develop and customize brain stimulation approaches for the rehabilitation of visuospatial neglect.

Does the EQ-5D usual activities dimension measure what it intends to measure? The relative importance of work, study, housework, family or leisure activities.

BACKGROUND: The EQ-5D is the most widely used generic preference-based health-related quality of life measure. It comprises five dimensions: mobility, self-care, usual activities, pain/discomfort and anxiety/depression. The usual activities dimension asks respondents to evaluate the severity of problems in their usual activities, such as work, study, housework, family or leisure activities. The primary aim of this study is to investigate whether the EQ-5D (five-level) usual activities dimension captures those activities that it intends to capture. We further assess the relative importance of each of these activities for the usual activities dimension. METHODS: Data include 7933 respondents from six countries: Australia, Canada, Germany, Norway, the UK, and the US. Logistic regression and ordinary least square regression models investigate the relationship between the usual activities dimension and its main predictors (work/study, housework, family, and leisure activities). A Shapley value decomposition method was applied to measure the relative importance of each predictor. RESULTS: Work/study, housework, family, and leisure activities were all significant (p < 0.001) determinants of usual activities dimension. The respective marginal contribution (in %) of housework, leisure, work/study and family to UA dimension (as a share of goodness-of-fit) is 28.0, 26.2, 20.8 and 14.7 in the logistic regression model. This finding is consistent when linear regression is used as an alternative model. CONCLUSIONS: The usual activities dimension in EQ-5D reflects the specific activities described to respondents. Therefore, the usual activities dimension measures what it really intends to measure.

Biodiversity, Shapley value and phylogenetic trees: some remarks.

This paper explores the main differences between the Shapley values of a set of taxa introduced by Haake et al. (J Math Biol 56:479-497, 2007. https://doi.org/10.1007/s00285-007-0126-2) and Fuchs and Jin (J Math Biol 71:1133-1147, 2015. https://doi.org/10.1007/s00285-014-0853-0), the latter having been found identical to the Fair Proportion index (Redding and Mooers in Conserv Biol 20:1670-1678, 2006. https://doi.org/10.1111/j.1523-1739.2006.00555.x). In line with Shapley (in: Kuhn, Tucker (eds) Contributions to to the theory of games, volume II, annals of mathematics studies 28, Princeton University Press, Princeton, 1953), we identify the cooperative game basis for each of these two classes of phylogenetic games and use them (i) to construct simple formulas for these two Shapley values and (ii) to compare these different approaches. Using the set of weights of a phylogenetic tree as a parameter space, we then discuss the conditions under which these two values coincide and, if they are not the same, revisit Hartmann's (J Math Biol 67:1163-1170, 2013. https://doi.org/10.1007/s00285-012-0585-y) convergence result. An example illustrates our main argument. Finally, we compare the species ranking induced by these two values. Considering the Kendall and the Spearman rank correlation coefficient, simulations show that these rankings are strongly correlated. These results are consistent with Wicke and Fischer (J Theor Biol 430:207-214, 2017. https://doi.org/10.1016/j.jtbi.2017.07.010), who reach similar conclusions with a different simulation method.