Qualitative probabilistic networks with reduced ambiguities

A Qualitative probabilistic network (QPN) is the qualitative abstraction of a Bayesian network that encodes variables and the qualitative influences between them. In order to make QPNs be practical for real-world representation and inference of uncertain knowledge, it is desirable to reduce ambiguities in general QPNs, including unknown qualitative influences and inference conflicts. In this paper, we first extend the traditional definition of qualitative influences by adopting the probabilistic threshold. In addition, we introduce probabilistic-rough-set-based weights to the qualitative influences. The enhanced network so obtained, called EQPN, is constructed from sample data. Finally, to achieve conflict-free EQPN inferences, we resolve the trade-offs by addressing the symmetry, transitivity and composition properties. Preliminary experiments verify the correctness and feasibility of our methods.     

Context-specific sign-propagation in qualitative probabilistic networks

Qualitative probabilistic networks are qualitative abstractions of probabilistic networks, summarising probabilistic influences by qualitative signs. As qualitative networks model influences at the level of variables, knowledge about probabilistic influences that hold only for specific values cannot be expressed. The results computed from a qualitative network, as a consequence, can be weaker than strictly necessary and may in fact be rather uninformative. We extend the basic formalism of qualitative probabilistic networks by providing for the inclusion of context-specific information about influences and show that exploiting this information upon reasoning has the ability to forestall unnecessarily weak results.     

基于定性互信息的定性概率网歧义性约简

针对符号传播算法在符号相反的两条平行路径上进行推理时常常产生歧义性,提出一种基于定性互信息的歧义性约简方法。首先,给出定性互信息的严格定义。然后,提出基于定性互信息影响强度的定性概率网,进一步区分影响强度,并证明具有强度的定性影响的对称性、传递性和复合性。最后在Antibiotics数据集上,通过与已有方法推理结果的对比实验,验证该歧义性约简方法的正确性和高效性。理论分析和实验结果表明,基于定性互信息的定性概率网既保留定性推理的简明性,又能够有效约简定性推理的歧义性。     

基于粗糙集的定性概率网推理冲突解决方法

定性概率是贝叶斯网的定性抽象,它以有向边上的定性影响代替贝叶斯网中的条件概率参数,描述了变量间增减的趋势,具有高效的推理机制。但定性概率网中信息丢失导致推理的过程中往往产生不确定信息,即推理结果产生冲突。以尽可能消除定性推理中的冲突为出发点,在构建定性概率网时,基于粗糙集属性依赖度理论求解出网中节点间的依赖度,以依赖度作为变量间定性影响的权重,并根据依赖度改进已有的定性概率网推理算法,从而解决定性概率网推理冲突。实例验证表明,该方法既保持了定性概率网高效推理的特性,又能有效解决冲突。     

基于论据系统的带权定性概率推理机

定性概率推理是不确定性推理领域的一种重要方法。将定性概率推理的论据系统方法和抽象系统方法二者合而为一,在定性概率推理机(QPR)的基础上提出基于论据系统的带权定性概率推理机(WQPR)。首先扩展了带权定性概率网的定义,讨论了带权定性影响的对称性;其次将带权定性概率推理融入到论据系统中,提出WQPR推理系统,相比QPR能够在更精确的尺度进行不确定性推理,并证明了系统的正确性与完备性。     

Bayesian network modelling through qualitative patterns

In designing a Bayesian network for an actual problem, developers need to bridge the gap between the mathematical abstractions offered by the Bayesian-network formalism and the features of the problem to be modelled. Qualitative probabilistic networks (QPNs) have been put forward as qualitative analogues to Bayesian networks, and allow modelling interactions in terms of qualitative signs. They thus have the advantage that developers can abstract from the numerical detail, and therefore the gap may not be as wide as for their quantitative counterparts. A notion that has been suggested in the literature to facilitate Bayesian-network development is causal independence. It allows exploiting compact representations of probabilistic interactions among variables in a network. In the paper, we deploy both causal independence and QPNs in developing and analysing a collection of qualitative, causal interaction patterns, called QC patterns. These are endowed with a fixed qualitative semantics, and are intended to offer developers a high-level starting point when developing Bayesian networks.     

CONSTRUCTION OF BELIEF AND DECISION NETWORKS

We describe a representation and set of inference techniques for the dynamic construction of probabilistic and decision-theoretic models expressed as networks. In contrast to probabilistic reasoning schemes that rely on fixed models, we develop a representation that implicitly encodes a large number of possible model structures. Based on a particular query and state of information, the system constructs a customized belief net for that particular situation. We develop an interpretation of the network construction process in terms of the implicit networks encoded in the database. A companion method for constructing belief networks with decisions and values (decision networks) is also developed that uses sensitivity analysis to focus the model building process. Finally, we discuss some issues of control of model construction and describe examples of constructing networks.     

PREPROCESSING RULES FOR TRIANGULATION OF PROBABILISTIC NETWORKS*

Currently, the most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre‐processing can help in finding good triangulations for probabilistic networks, that is, triangulations with a maximum clique size as small as possible. We provide a set of rules for stepwise reducing a graph, without losing optimality. This reduction allows us to solve the triangulation problem on a smaller graph. From the smaller graph's triangulation, a triangulation of the original graph is obtained by reversing the reduction steps. Our experimental results show that the graphs of some well‐known real‐life probabilistic networks can be triangulated optimally just by preprocessing; for other networks, huge reductions in their graph's size are obtained.     

一种信度网推理的并行计算模型

基于概率知识表达的信度网已成为人工智能中非确定知识表达和推理的研究热点。推理算法是信度网学习和应用的基础。该文提出了一种基于经典Polytree算法的推理计算模型。该模型表达清楚,计算过程容易控制,并能够简单地映射到并行机结构上。该文首先介绍了模型在单联通网络下的计算步骤,然后将模型引入到多联通网络上。     

带权重的定性贝叶斯网

定性贝叶斯网使用定性的影响标记表示变量之间的影响关系,但不能表达影响力的强弱,在推理过程中容易出现不确定的结果.研究了带权重的定性贝叶斯网,权重是一个[0,1]区间内的数值,用以表达影响力的强弱,修正了推理中的运算规则,并设计了权重标杆方便专家给出权重,保持了定性贝叶斯网络建模过程的简易性,同时提高了推理精度.     

An adaptive reasoning approach towards efficient ordering of composite hypotheses

A Bayesian network is a knowledge representation framework for encoding both qualitative and quantitative probabilistic dependencies among a set of propositional (or random) variables. An important type of probabilistic inference in a Bayesian network is the derivation of the most probable composite hypotheses — a set of hypotheses composed of multiple variables in a network. Such a type of probabilistic inference, however, is computationally intractable. In this paper an adaptive reasoning approach based on qualitative interval arithmetic is proposed as a method of dealing with the computational problem. Using this approach, a qualitative boundary, which reflects the upper and lower limits of a posterior likelihood, can be derived for each composite hypothesis. The advantage ofbounding each composite hypothesis qualitatively is that the quantitative values of the posterior likelihoods are not all necessary in the course of an inference. Consequently, an exhaustive evaluation can be avoided. The complexity of the proposed approach can be demonstrated to be no worse than that of a direct computation and in some cases, the computation is only a small fraction of that required in a straightforward direct computation.This work was supported in part by a grant to Queens College from the General Research Branch, National Institute of Health under grant No. RR-07064, and in part by a grant from the City University of New York PSC-CUNY Research Award Program.     

概率图模型推理方法的研究进展

近年来概率图模型已成为不确定性推理的研究热点,在人工智能、机器学习与计算机视觉等领域有广阔的应用前景.根据网络结构与查询问题类型的不同,系统地综述了概率图模型的推理算法.首先讨论了贝叶斯网络与马尔可夫网络中解决概率查询问题的精确推理算法与近似推理算法,其中主要介绍精确推理中的VE算法、递归约束算法和团树算法,以及近似推理中的变分近似推理和抽样近似推理算法,并给出了解决MAP查询问题的常用推理算法;然后分别针对混合网络的连续与混合情况阐述其推理算法,并分析了暂态网络的精确推理、近似推理以及混合情况下的推理;最后指出了概率图模型推理方法未来的研究方向.     

An Approximate Algorithm for Min‐Based Possibilistic Networks

Min‐based (or qualitative) possibilistic networks are important tools to efficiently and compactly represent and analyze uncertain information. Inference is a crucial task in min‐based networks, which consists of propagating information through the network structure to answer queries. Exact inference computes posteriori possibility distributions, given some observed evidence, in a time proportional to the number of nodes of the network when it is simply connected (without loops). On multiply connected networks (with loops), exact inference is known as a hard problem. This paper proposes an approximate algorithm for inference in min‐based possibilistic networks. More precisely, we adapt the well‐known approximate algorithm Loopy Belief Propagation (LBP) on qualitative possibilistic networks. We provide different experimental results that analyze the convergence of possibilistic LBP.     

Complex Probabilistic Modeling with Recursive Relational Bayesian Networks

A number of representation systems have been proposed that extend the purely propositional Bayesian network paradigm with representation tools for some types of first-order probabilistic dependencies. Examples of such systems are dynamic Bayesian networks and systems for knowledge based model construction. We can identify the representation of probabilistic relational models as a common well-defined semantic core of such systems.Recursive relational Bayesian networks (RRBNs) are a framework for the representation of probabilistic relational models. A main design goal for RRBNs is to achieve greatest possible expressiveness with as few elementary syntactic constructs as possible. The advantage of such an approach is that a system based on a small number of elementary constructs will be much more amenable to a thorough mathematical investigation of its semantic and algorithmic properties than a system based on a larger number of high-level constructs. In this paper we show that with RRBNs we have achieved our goal, by showing, first, how to solve within that framework a number of non-trivial representation problems. In the second part of the paper we show how to construct from a RRBN and a specific query, a standard Bayesian network in which the answer to the query can be computed with standard inference algorithms. Here the simplicity of the underlying representation framework greatly facilitates the development of simple algorithms and correctness proofs. As a result we obtain a construction algorithm that even for RRBNs that represent models for complex first-order and statistical dependencies generates standard Bayesian networks of size polynomial in the size of the domain given in a specific application instance.     

基于超结构的BN随机搜索学习算法

近年来,贝叶斯网络(Bayesian network, BN)在不确定性知识表示与概率推理方面发挥着越来越重要的作用.其中,BN结构学习是BN推理中的重要问题.然而,在当前BN结构的2阶段混合学习算法中,大多存在一些问题：第1阶段无向超结构学习中存在容易丢失弱关系的边的问题;第2阶段的爬山搜索算法存在易陷入局部最优的问题.针对这2个问题,首先采用Opt01ss算法学习超结构,尽可能地避免出现丢边现象;然后给出基于超结构的搜索算子,分析初始网络的随机选择规则和对初始网络随机优化策略,重点提出基于超结构的随机搜索的SSRandom结构学习算法,该算法一定程度上可以很好地跳出局部最优极值;最后在标准Survey, Asia,Sachs网络上,通过灵敏性、特效性、欧几里德距离和整体准确率4个评价指标,并与已有3种混合学习算法的实验对比分析,验证了该学习算法的良好性能.     

带权定性影响图

定性影响图是具有精确概率和效用的影响图的定性抽象。在定性影响图中,节点之间的影响关系使用定性符号描述,这种符号描述简化了不确定知识的表示,降低了影响图建模的难度,加速了不确定知识的推理。但是,定性影响图在抽象过程中损失了部分信息,导致定性影响图在评价过程中会产生不确定结果,阻碍了定性影响图的广泛应用。以加权的思想扩展定性影响图,使扩展的定性影响图中每个定性影响都带有一个表示节点间影响强弱的数值权值,在评价过程中根据定性影响权值的比较来减少不确定结果的产生,从而扩大定性影响图的应用范围。     

Capturing a Qualitative Model of Network Performance and Predicting Behavior

This paper describes a method for constructingbehavior models of communication networks. The methodutilizes archived quantitative performance data createdby a network management platform to create a Quantitative/Qualitative (Q²)Dynamic System representation. The Q²representation captures the predominant qualitative(symbolic) states of the network, qualitative inputevents and transitions among the states resulting from these events. Thissymbolic model allows the network manager to understandthe current system behavior, and predict future possiblebehaviors. We evaluated the method on two sets of archive data. The method shows promise foruse in network management, including network monitoring,fault detection, prognostication andavoidance.     

基于神经网络专家系统的研究与实现

针对传统专家系统推理能力弱和智能水平低等不足,本文采用神经网络方法解决了传统专家系统在知识表示和知识获取等方面的问题。本文从描述传统专家系统几点不足出发,详细阐述了神经网络专家系统的基本原理和框架结构,最后选取三层BP神经网络模型,给出了钻井故障诊断系统的神经网络专家系统的实现。     

A Bayesian Method for the Induction of Probabilistic Networks from Data

This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. We extend the basic method to handle missing data and hidden (latent) variables. We show how to perform probabilistic inference by averaging over the inferences of multiple belief networks. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. Finally, we relate the methods in this paper to previous work, and we discuss open problems.