Reinvestigating Dempster's Idea on Evidence Combination

In this paper, we investigate the problem encountered by Dempster's combination rule in view of Dempster's original combination framework. We first show that the root of Dempster's combination rule (defined and named by Shafer) is Dempster's original idea on evidence combination. We then argue that Dempster's original idea on evidence combination is, in fact, richer than what has been formulated in the rule. We conclude that, by strictly following what Dempster has suggested, there should be no counterintuitive results when combining evidence. Received 3 December 1998 / Revised 30 June 1999 / Accepted in revised form 7 February 2000     

信任函数组合与局部冲突处理

在证据理论框架中,数据融合是将几个来自不同证据源的信任函数组合成一个信任函数,Dempster组合规则是人们常用的方法,但由于此规则是通过按比例放大组合后焦元的基本信任指派值而使其满足信任函数的标准定义,尽管这一标准化方法有逻辑上的解释,但还是招致诸多批评,并提出了一些修正的组合规则。Dempster组合规则尤其在较强冲突情形下其组合结果是不符合常理的,因此不同证据源的冲突处理是信息融合的主要问题。该文通过分析比较已有的主要组合规则,提出了一种处理冲突的新方法--局部冲突处理法,此方法可克服已有方法的缺点,而且组合结果更加合理。     

Dempster证据合成法则的通用实现方法

证据推理是不确定性推理的一种重要方法,而Dcmpstcr合成法则是进行证据推理的核心。针对目前Dcmp- stcr证据合成法则的算法实现不能处理合成结果的焦元为多个假设或命题的集合、近似算法的计算不够精确等问题, 提出通过位向量表示识别框架子集,并利用线性表、平衡树等数据结构实现证据合成的3种精确、通用算法。理论分 析与仿真实验表明,所实现的算法是有效的。     

A comprehensive comparison between generalized incidence calculus and the Dempster-Shafer theory of evidence

Dealing with uncertainty problems in intelligent systems has attracted a lot of attention in the AI community. Quite a few techniques have been proposed. Among them, the Dempster-Shafer theory of evidence (DS theory) has been widely appreciated. In DS theory, Dempster's combination rule plays a major role. However, it has been pointed out that the application domains of the rule are rather limited and the application of the theory sometimes gives unexpected results. We have previously explored the problem with Dempster's combination rule and proposed an alternative combination mechanism in generalized incidence calculus. In this paper we give a comprehensive comparison between generalized incidence calculus and the Dempster-Shafer theory of evidence. We first prove that these two theories have the same ability in representing evidence and combining DS-independent evidence. We then show that the new approach can deal with some dependent situations while Dempster's combination rule cannot. Various examples in the paper show the ways of using generalized incidence calculus in expert systems.     

Generalized rules for combination and joint training of classifiers

Classifier combination has repeatedly been shown to provide significant improvements in performance for a wide range of classification tasks. In this paper, we focus on the problem of combining probability distributions generated by different classifiers. Specifically, we present a set of new combination rules that generalize the most commonly used combination functions, such as the mean, product, min, and max operations. These new rules have continuous and differentiable forms, and can thus not only be used for combination of independently trained classifiers, but also as objective functions in a joint classifier training scheme. We evaluate both of these schemes by applying them to the combination of phone classifiers in a speech recognition system. We find a significant performance improvement over previously used combination schemes when jointly training and combining multiple systems using a generalization of the product rule.     

基于向量冲突表示方法的证据组合规则

针对Dempster组合规则在高冲突证据融合的情况下常常会得到违背直觉的结果,提出了一种基于向量冲突表示方法的Dempster(VCRD)组合规则。首先,通过实例分析了冲突因子和Jousselme距离存在的不足;然后,利用证据向量的相似性和差异性共同衡量证据之间的冲突程度,通过证据之间的冲突程度确定修正证据的权重因子,对融合证据进行预处理;最后,利用Dempster组合规则进行融合。理论分析和仿真实验结果表明:与Dempster组合规则及其它改进算法相比,VCRD组合规则能够合理地处理高冲突证据情况下的融合问题,降低了决策风险。     

Geometry of Dempster''s rule of combination

In this paper, we analyze Shafer's belief functions (BFs) as geometric entities, focusing in particular on the geometric behavior of Dempster's rule of combination in the belief space, i.e., the set Stheta of all the admissible BFs defined over a given finite domain theta. The study of the orthogonal sums of affine subspaces allows us to unveil a convex decomposition of Dempster's rule of combination in terms of Bayes' rule of conditioning and prove that under specific conditions orthogonal sum and affine closure commute. A direct consequence of these results is the simplicial shape of the conditional subspaces , i.e., the sets of all the possible combinations of a given BF s. We show how Dempster's rule exhibits a rather elegant behavior when applied to BFs assigning the same mass to a fixed subset (constant mass loci). The resulting affine spaces have a common intersection that is characteristic of the conditional subspace, called focus. The affine geometry of these foci eventually suggests an interesting geometric construction of the orthogonal sum of two BFs.     

非单点证据体数据融合的Dempster组合规则适用性评价方法

针对待融合的证据体包含基本概率分配值相差较大的非单点证据时,基于pignistic距离的Dempster组合规则适用性评价方法判定结果存在模糊性甚至不准确的问题,提出了一种表示证据体之间关联性的改进pignistic距离,并将改进的pignistic距离与经典冲突系数相结合,提出了对Dempster组合规则适用性评价的新方法。在新方法中,定义了一种新的证据体冲突衡量系数用于判定Dempster规则的适用性。当经典冲突系数为0时,新系数与改进pignistic距离一致;当经典冲突系数不为0时,新系数与改进pignistic距离和经典冲突系数之和的平均值一致。算例分析的结果表明,与基于pignistic距离的Dempster规则适用性评价方法相比,新的基于改进pignistic距离的Dempster组合规则适用性评价方法有较好的适用性和合理性。     

Dempster组合规则适用性分析

针对传统冲突系数识别证据冲突存在漏识、误识和冲突系数值会累加增大等问题,采用pignistic变换后得到 的概率赋值函数之间的距离,结合传统冲突量化标准,研究了Dempst er组合规则适用性判断方法。通过与Liu判断 Dcmpstcr组合规则适用性方法的对比结果表明,本方法对Dcmpstcr组合规则适用判断有较好的适用性与合理性。     

Dempster规则的有效性和限制

1 引言 Dempster-Shafer证据理论(以下简称证据理论)是在A.P.Dempster提出的“上、下概率”及其合成规则的基础上由G.Shafer在其1976年出版的专著《证据的数学理论》中建立起来的。80年代初,SRI的J.Lowrance等人将证据理论引入人工智能;J.Gordon和E.Shortliffe在专家系统的框架中研究了证据推理。此后,证据理论逐渐发展成为一类重要的不确定性推理方法。现在,基于证据理论的不确定性处理方法已是设计专家系统及其它智能系统的标准工具之一。     

一种有监督学习证据理论分类器

经典的证据理论不包括从实例中学习基本信度分配的机制,因此应用范围受到一定限制。通过在证据理论中引入神经网络的学习机制,该文提出了一种有监督学习证据理论分类器。该分类器使用一种经过修改的Widrow-Hoff学习规则从训练实例中学习基本信度分配信息。新实例到来后,该分类器在所学基本信度分配的基础上,使用证据理论合成公式对新实例作分类。新分类器拓展了证据理论的应用领域。实验结果表明该分类器是有效的。     

Building contextual classifiers by integrating fuzzy rule based classification technique and k-nn method for credit scoring

Credit-risk evaluation is a very challenging and important problem in the domain of financial analysis. Many classification methods have been proposed in the literature to tackle this problem. Statistical and neural network based approaches are among the most popular paradigms. However, most of these methods produce so-called “hard” classifiers, those generate decisions without any accompanying confidence measure. In contrast, “soft” classifiers, such as those designed using fuzzy set theoretic approach; produce a measure of support for the decision (and also alternative decisions) that provides the analyst with greater insight. In this paper, we propose a method of building credit-scoring models using fuzzy rule based classifiers. First, the rule base is learned from the training data using a SOM based method. Then the fuzzy k-nn rule is incorporated with it to design a contextual classifier that integrates the context information from the training set for more robust and qualitatively better classification. Further, a method of seamlessly integrating business constraints into the model is also demonstrated.     

论Dempster-Shafer理论的一个悖论

Kyburg指出,在Dempster-Shafer（D-S）理论中应用Dempster组合规则组合某些基本概率指派将导致悖论。基于Shafer的D-S理论解释,我们可以利用概率函数来表达该理论的基本概念和组合规则。在此基础上,本文分析这一悖论产生的原因。     

基于注意力与多模态混合融合的谣言检测方法

社交媒体内容结构具有复杂性,大量虚假信息掺杂在真实内容中,或者在真实图片上配以杜撰的文字内容,导致基于单个模态的方法难以有效检测谣言。提出基于注意力机制与Dempster’s组合规则的混合融合方法。通过新增用户模态,提取文本、视觉和用户3个模态的特征向量,利用注意力机制对词语和视觉进行双向匹配,给予对谣言检测具有更多贡献的词语和视觉神经元更大的权值。在前后期融合均加入注意力机制,实现特征和决策的自动加权,并使用Dempster's组合规则实现混合融合。在真实的中文Weibo数据集和外文Twitter数据集上的实验结果表明,该方法准确率分别达到97.44%和92.35%,准确率和F1-score指标均高于基准方法和多模态方法。     

A flexible rule for evidential combination in Dempster–Shafer theory of evidence

Dempster’s combination rule in Dempster–Shafer theory of evidence is widely used to combine multiple pieces of evidence. However, when the evidence is severely conflicting, the result could be counter-intuitive. Thus, many alternative combination rules have been proposed to address this issue. Nevertheless, the existing ones sometimes behave not very well. This may be because they do not hold some essential properties. To this end, this paper firstly identifies some of the important properties. Then, following the cues from these properties, we propose a novel evidential combination rule as a remediation of Dempster’s combination rule in Dempster–Shafertheory. Our new rule is based on the concept of complete conflict (we introduced in this paper), Dempster’s combination rule, and the concept of evidence weight. Moreover, we illustrate the effectiveness of our new rule by using it to successfully resolve well-known Zadeh’s counter-example, which is against Dempster’s combination rule. Finally, we confirm the advantages of our method over the existing methods through some examples.     

On the Dempster-Shafer evidence theory and non-hierarchicalaggregation of belief structures

The Dempster's rule of combination is a widely used technique to integrate evidence collected from different sources. In this paper, it is shown that the values of certain functions defined on a family of belief structures decrease (by scale factors depending on the degree of conflict) when the belief structures are combined according to the Dempster's rule. Similar results also hold when an arbitrary belief structure is prioritized while computing the combination. Furthermore, the length of the belief-plausibility interval is decreased during a nonhierarchical aggregation of belief structures. Several types of inheritance networks are also proposed each of which allows considerable flexibility in the choice of prioritization     

证据推理的鲁棒性研究

在处理不确定信息的方法中,证据推理性能突出、应用广泛,它的鲁棒性分析十分必要.首先基于证据推理的目的和要求,给出证据推理鲁棒性的定义,并提出冲突率的新概念,以此为尺度对Dempster规则、加权分配冲突法和吸收法的鲁棒性进行了深入分析,证明了各方法鲁棒性结果.仿真结果表明改进的组合规则鲁棒性能得到了明显增强.最后给出证据推理的一般情形的鲁棒性分析.     

Multimodal speaker identification using an adaptive classifier cascade based on modality reliability

We present a multimodal open-set speaker identification system that integrates information coming from audio, face and lip motion modalities. For fusion of multiple modalities, we propose a new adaptive cascade rule that favors reliable modality combinations through a cascade of classifiers. The order of the classifiers in the cascade is adaptively determined based on the reliability of each modality combination. A novel reliability measure, that genuinely fits to the open-set speaker identification problem, is also proposed to assess accept or reject decisions of a classifier. A formal framework is developed based on probability of correct decision for analytical comparison of the proposed adaptive rule with other classifier combination rules. The proposed adaptive rule is more robust in the presence of unreliable modalities, and outperforms the hard-level max rule and soft-level weighted summation rule, provided that the employed reliability measure is effective in assessment of classifier decisions. Experimental results that support this assertion are provided.     

一种基本概率指派的模糊生成及其在数据融合中的应用

DS证据组合规则可以在没有先验信息的情况下进行融合,这一优点使得DS证据理论在多传感器融合系统中应用非常广泛.但是各个证据的基本概率指派如何生成仍然是一个有待解决的问题.本文基于模糊匹配,提出了一种基本概率指派生成方法,并应用到多传感器目标识别中.用一个多传感器目标识别的实验表明:所提出的方法可以合理地生成基本概率指派,能够准确的识别目标.     

Belief function combination and conflict management

Within the framework of evidence theory, data fusion consists in obtaining a single belief function by the combination of several belief functions resulting from distinct information sources. The most popular rule of combination, called Dempster's rule of combination (or the orthogonal sum), has several interesting mathematical properties such as commutativity or associativity. However, combining belief functions with this operator implies normalizing the results by scaling them proportionally to the conflicting mass in order to keep some basic properties. Although this normalization seems logical, several authors have criticized it and some have proposed other solutions. In particular, Dempster's combination operator is a poor solution for the management of the conflict between the various information sources at the normalization step. Conflict management is a major problem especially during the fusion of many information sources. Indeed, the conflict increases with the number of information sources. That is why a strategy for re-assigning the conflicting mass is essential. In this paper, we define a formalism to describe a family of combination operators. So, we propose to develop a generic framework in order to unify several classical rules of combination. We also propose other combination rules allowing an arbitrary or adapted assignment of the conflicting mass to subsets.