Shapley值法的改进及其应用研究

为了求解没有哑元的合作对策问题,以经典Shapley值法为基础,提出了改进的Shapley值求解模型,并通过证明和推理对该改进Shapley值解进行了描述和刻画,结果表明:改进的Shapley函数和经典Shapely函数在形式上具有一致性,可以认为:改进的Shapley函数是经典Shapely函数在模糊领域的一个自然延续和拓展。在此基础上,以单个制造商、单个分销商和单个零售商构成的三级供应链为背景,将改进Shapley值法运用到其利润分配问题中,并用一个算例说明了该改进Shapley解的实用性和可行性。     

基于Shapley值修正的服务供应链系统利益分配研究

基于Shapley值的利益分配策略是研究利益分配的有效方法,但其不考虑系统成员在投入等因素方面的差异性,因此在服务供应链系统利益分配过程中,需要进行修正。通过分别考虑投入因素、努力因素和风险因素对其进行修正的基础上,建立了基于Shapely值的服务供应链系统利益分配综合修正模型进行利益分配。     

要素双重模糊下的合作博弈Shapley值的算法

考虑到现实应用中,局中人可能以不同的参与度参加到不同的联盟中,并且他们在合作之前不确定不同合作策略选择下的收益,则在传统合作博弈中应用模糊数学理论。基于Choquet积分,将支付函数和参与度拓展为模糊数,给出要素双重模糊下的模糊合作博弈的定义和模糊合作博弈Shapley值的定义。应用模糊结构元理论,构造了要素双重模糊下的模糊合作博弈的Shapley值,使模糊Shapley值的隶属函数得到解析表达。通过一个算例,来说明该模型的具体应用。可以看出,该研究方法和结论易掌握、推广,使模糊合作博弈理论可以更广泛地应用到现实生活中。     

基于动态模糊联盟合作博弈的区间模糊Shapley值

利用模糊数学相关理论,针对n人合作博弈中支付函数是模糊三角函数的情形,对经典Shapley值提出的三条公理进行了拓展,并构造了区间模糊Shapley值。考虑到盟友在合作结束后需要对具体的联盟收益进行分配,利用构造的区间模糊Shapley值隶属函数给出了确定的收益分配方案。最后利用实例对该方法的有效性和可行性进行了说明。     

基于Shapley值的自组网合作机制分析

在无线移动自组网中,每个节点都独立进行决定,不可能完全自发合作。针对该问题,基于移动自组网的特殊性,将节点间的信息传递看作二人博弈,提出一个约束协议,使节点只有在合作时才能到达各自的收益最大,且使网络性能最优。同时分析网络传输失败原因是网络噪声干扰还是参与者的恶意行为。     

小样本条件下基于属性权重Shapley值分配的粗糙集决策模型

小样本条件下,根据粗糙集理论构建的决策规则受数据来源偶然性误差影响较大,个别数据样本难以反映真实知识关系.为解决小样本条件下粗糙集决策规则可信度未知的问题,提出信息区分量、属性影响方向等概念,运用Shapley值法进行属性权重分配,求取每个属性对决策结果的影响方向,进而得出决策规则的参考信度,以寻求真实可信且适合工程实际的决策规则.实例分析论证了所提方法的可行性以及对数据来源误差的分辨能力.     

基于改进Shapley值的四级供应链利润分配研究

为求解供应链利润分配问题,以经典Shapley值法为基础,将利润分配视为没有哑元的合作对策问题,提出改进的Shapley值模型,通过证明和推理对该改进Shapley值解进行描述和刻画,运用该模型求解四级供应链利润分配问题,并用一个算例说明该改进Shapley解的实用性和可行性。结果表明,改进的Shapley函数和经典Shapley函数在形式上具有一致性,是经典Shapley函数在模糊领域的一个自然延续和拓展,能够有效解决供应链利润分配问题。     

Shapley值法在配电网供电能力计算中的应用

应用Shapley值法,在售电侧放开后各售电公司利益均衡的情况下,评估电网的供电能力.首先,在研究合作博弈的利益分配模型基础上,计算各售电商成员的利润分配结果;然后,反推各售电商的购电量;最后,提岀考虑售电公司利益均衡的配电网供电能力计算方法.通过仿真算例分析,有效地解决了电力市场环境下的供电能力计算.     

机器学习模型可解释性方法、应用与安全研究综述

尽管机器学习在许多领域取得了巨大的成功,但缺乏可解释性严重限制了其在现实任务尤其是安全敏感任务中的广泛应用.为了克服这一弱点,许多学者对如何提高机器学习模型可解释性进行了深入的研究,并提出了大量的解释方法以帮助用户理解模型内部的工作机制.然而,可解释性研究还处于初级阶段,依然还有大量的科学问题尚待解决.并且,不同的学者解决问题的角度不同,对可解释性赋予的含义也不同,所提出的解释方法也各有侧重.迄今为止,学术界对模型可解释性仍缺乏统一的认识,可解释性研究的体系结构尚不明确.在综述中,回顾了机器学习中的可解释性问题,并对现有的研究工作进行了系统的总结和科学的归类.同时,讨论了可解释性相关技术的潜在应用,分析了可解释性与可解释机器学习的安全性之间的关系,并且探讨了可解释性研究当前面临的挑战和未来潜在的研究方向,以期进一步推动可解释性研究的发展和应用.     

Shapley值的LTE系统下行QoS感知资源调度

针对长期演进（Long Term Evolution,LTE）系统下行链路多用户业务传输过程中实时（Real-Time,RT）业务与非实时（Non-Real-Time,NRT）业务传输性能需求问题,提出一种基于合作博弈论Shapley值的信道资源初始控制方法。该方法在MAC（Media Access Control）层根据业务传输数据量大小来计算联盟边界贡献值,然后利用Shapley值来计算各业务占用的信道资源,再根据所分配的信道资源进行RB（Resource Block）调度。链路仿真表明,该方法在保证各业务时延与丢包率的基础上,提升了非实时业务的传输性能,在用户数量从5变化到50的条件下,对比DPVT-MLWDF（Delay Priority Virtual Token-Modified Largest Weighted Delay First）算法,非实时业务的吞吐量平均增加了38.05%,公平性提升了12.51%。实验结果表明,所提出的区分业务的信道资源控制方法在多用户业务条件下保证了实时业务传输性能,提升了非实时业务的吞吐量及公平性,明显优于对比算法。     

Characterizations of a Shapley value for multichoice games

The main focus of this paper is on a Shapley value for multichoice games introduced by van den Nouweland et al. (ZOR–Math. Meth. Oper. Res. 41?:?289–311, 1995). Here we provide several characterizations from traditional game theory and redefine them in the framework of multichoice games. Meanwhile, the relationship between core and this Shapley value for multichoice games is discussed. When multichoice games are convex, this Shapley value is a multichoice population monotonic allocation scheme (MPMAS).     

A linear approximation method for the Shapley value

The Shapley value is a key solution concept for coalitional games in general and voting games in particular. Its main advantage is that it provides a unique and fair solution, but its main drawback is the complexity of computing it (e.g., for voting games this complexity is #p-complete). However, given the importance of the Shapley value and voting games, a number of approximation methods have been developed to overcome this complexity. Among these, Owen's multi-linear extension method is the most time efficient, being linear in the number of players. Now, in addition to speed, the other key criterion for an approximation algorithm is its approximation error. On this dimension, the multi-linear extension method is less impressive. Against this background, this paper presents a new approximation algorithm, based on randomization, for computing the Shapley value of voting games. This method has time complexity linear in the number of players, but has an approximation error that is, on average, lower than Owen's. In addition to this comparative study, we empirically evaluate the error for our method and show how the different parameters of the voting game affect it. Specifically, we show the following effects. First, as the number of players in a voting game increases, the average percentage error decreases. Second, as the quota increases, the average percentage error decreases. Third, the error is different for players with different weights; players with weight closer to the mean weight have a lower error than those with weight further away. We then extend our approximation to the more general k-majority voting games and show that, for n players, the method has time complexity O(k²n) and the upper bound on its approximation error is .     

On the measure of conflicts: Shapley Inconsistency Values

There are relatively few proposals for inconsistency measures for propositional belief bases. However inconsistency measures are potentially as important as information measures for artificial intelligence, and more generally for computer science. In particular, they can be useful to define various operators for belief revision, belief merging, and negotiation. The measures that have been proposed so far can be split into two classes. The first class of measures takes into account the number of formulae required to produce an inconsistency: the more formulae required to produce an inconsistency, the less inconsistent the base. The second class takes into account the proportion of the language that is affected by the inconsistency: the more propositional variables affected, the more inconsistent the base. Both approaches are sensible, but there is no proposal for combining them. We address this need in this paper: our proposal takes into account both the number of variables affected by the inconsistency and the distribution of the inconsistency among the formulae of the base. Our idea is to use existing inconsistency measures in order to define a game in coalitional form, and then to use the Shapley value to obtain an inconsistency measure that indicates the responsibility/contribution of each formula to the overall inconsistency in the base. This allows us to provide a more reliable image of the belief base and of the inconsistency in it.     

Polynomial calculation of the Shapley value based on sampling

In this paper we develop a polynomial method based on sampling theory that can be used to estimate the Shapley value (or any semivalue) for cooperative games. Besides analyzing the complexity problem, we examine some desirable statistical properties of the proposed approach and provide some computational results.     

Parallel characterizations of a generalized Shapley value and a generalized Banzhaf value for cooperative games with level structure of cooperation

We present parallel characterizations of two different values in the framework of restricted cooperation games. The restrictions are introduced as a finite sequence of partitions defined on the player set, each of them being coarser than the previous one, hence forming a structure of different levels of a priori unions. On the one hand, we consider a value first introduced in Ref. [18], which extends the Shapley value to games with different levels of a priori unions. On the other hand, we introduce another solution for the same type of games, which extends the Banzhaf value in the same manner. We characterize these two values using logically comparable properties.     

随机森林的可解释性可视分析方法研究

由于随机森林算法在很多情况下都以“黑盒”的方式存在,对于用户而言,参数调整,训练甚至最终构建的模型细节是隐蔽的,这导致了随机森林模型的可解释性非常差,在一定程度上阻碍了该模型在一些诸如医学诊断、司法、安全领域等需要透明化和可解释需求比较高的领域使用。影响该模型可解释性挑战主要来源于特征选择和数据的随机性。同时随机森林包含许多决策树,用户很难理解和比较所有决策树的结构和属性。为了解决上述问题,设计并实现了可视分析系统FORESTVis,该系统包括树视图、部分依赖图、t-SNE投影图、特征视图等多个交互式可视化组件,借助该系统,相关研究人员和从业人员可以直观地了解随机森林的基本结构和工作机制,并协助用户对模型的性能进行评估。使用Kaggle公开数据集上进行案例分析,验证了该方法的可行性和有效性。     

一种基于图模型的网络攻击溯源方法

随着信息技术的飞速发展,网络攻击事件频发,造成了日益严重的经济损失或社会影响.为了减少损失或预防未来潜在的攻击,需要对网络攻击事件进行溯源以实现对攻击者的挖掘追责.当前的溯源过程主要依赖于人工完成,效率低下.面对日益增加的海量溯源数据和日趋全面的溯源建模分析维度,亟需半自动化或自动化的网络攻击者挖掘方法.提出一种基于图...