Learning symmetric causal independence models

Causal independence modelling is a well-known method for reducing the size of probability tables, simplifying the probabilistic inference and explaining the underlying mechanisms in Bayesian networks. Recently, a generalization of the widely-used noisy OR and noisy AND models, causal independence models based on symmetric Boolean functions, was proposed. In this paper, we study the problem of learning the parameters in these models, further referred to as symmetric causal independence models. We present a computationally efficient EM algorithm to learn parameters in symmetric causal independence models, where the computational scheme of the Poisson binomial distribution is used to compute the conditional probabilities in the E-step. We study computational complexity and convergence of the developed algorithm. The presented EM algorithm allows us to assess the practical usefulness of symmetric causal independence models. In the assessment, the models are applied to a classification task; they perform competitively with state-of-the-art classifiers.     

MEBN: A language for first-order Bayesian knowledge bases

Although classical first-order logic is the de facto standard logical foundation for artificial intelligence, the lack of a built-in, semantically grounded capability for reasoning under uncertainty renders it inadequate for many important classes of problems. Probability is the best-understood and most widely applied formalism for computational scientific reasoning under uncertainty. Increasingly expressive languages are emerging for which the fundamental logical basis is probability. This paper presents Multi-Entity Bayesian Networks (MEBN), a first-order language for specifying probabilistic knowledge bases as parameterized fragments of Bayesian networks. MEBN fragments (MFrags) can be instantiated and combined to form arbitrarily complex graphical probability models. An MFrag represents probabilistic relationships among a conceptually meaningful group of uncertain hypotheses. Thus, MEBN facilitates representation of knowledge at a natural level of granularity. The semantics of MEBN assigns a probability distribution over interpretations of an associated classical first-order theory on a finite or countably infinite domain. Bayesian inference provides both a proof theory for combining prior knowledge with observations, and a learning theory for refining a representation as evidence accrues. A proof is given that MEBN can represent a probability distribution on interpretations of any finitely axiomatizable first-order theory.     

IDENTIFIABILITY IN CAUSAL BAYESIAN NETWORKS: A GENTLE INTRODUCTION

In this article we describe an important structure used to model causal theories and a related problem of great interest to semi-empirical scientists. A causal Bayesian network is a pair consisting of a directed acyclic graph (called a causal graph) that represents causal relationships and a set of probability tables, that together with the graph specify the joint probability of the variables represented as nodes in the graph. We briefly describe the probabilistic semantics of causality proposed by Pearl for this graphical probabilistic model, and how unobservable variables greatly complicate models and their application. A common question about causal Bayesian networks is the problem of identifying causal effects from nonexperimental data, which is called the identifability problem. In the basic version of this problem, a semi-empirical scientist postulates a set of causal mechanisms and uses them, together with a probability distribution on the observable set of variables in a domain of interest, to predict the effect of a manipulation on some variable of interest. We explain this problem, provide several examples, and direct the readers to recent work that provides a solution to the problem and some of its extensions. We assume that the Bayesian network structure is given to us and do not address the problem of learning it from data and the related statistical inference and testing issues.     

对弧进行删除的Bayes网络近似方法

弧的删除是一种对Bayes网络模型进行近似的方法。文中以Kullback-Leibler偏差作为近似网络和原网络概率分布误差的测度,给出了近似网络在此测度意义下的最优参数。同时,也给出了通过对原网络删除多条弧进行近似的启发式算法,当给定一个误差上界时,可以使用此算法寻找满足误差要求的近似网络。     

由Markov网到Bayesian网

Markov网（马尔可夫网）是类似于Bayesian网（贝叶斯网）的另一种进行不确定性揄的有力工具，Markov网是一个无向图，而Bayesian网是一个有向无环图，发现Markov网不需要发现边的方向，因此要比发现Bayesian网容易得多，提出了一种通过发现Markov网得到等价的Bayesian网的方法，首先利用信息论中验证信息独立的一个重要结论，提出了一个基于依赖分析的边删除算法发现Markov网，该算法需O（n^2)次CI（条件独立）测试，CI测试的时间复杂度取决于由样本数据得到的联合概率函数表的大小，经证明，假如由样本数据得到的联合概率函数严格为正，则该算法发现的Markov网一定是样本的最小L图，由发现Markov网，根据表示的联合概率函数相等，得到与其等价的Bayesian网。     

Dynamic Uncertain Causality Graph for Knowledge Representation and Reasoning: Discrete DAG Cases

Developed from the dynamic causality diagram (DCD) model,a new approach for knowledge representation and reasoning named as dynamic uncertain causality graph (DUCG) is presented,which focuses on the co...     

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.     

基于贝叶斯网络的军事工程毁伤评估模型研究

应用贝叶斯网络理论在解决不确定性事件方面的推理优势,提出了基于贝叶斯网络的军事工程毁伤评估新方法。根据军事工程毁伤评估的系统特征与要求,提出了分解、转换、综合的系统建模规则,并引入贝叶斯网络原理,建立了运用贝叶斯网络进行军事工程毁伤评估系统建模的分析框架;在确定军事工程毁伤评估网络节点变量的基础上,以仿真计算数据为样本,确定网络结构和网络参数,寻找隐含的概率依赖关系和知识表达,构建军事工程毁伤评估置信模型。通过实例验证了用贝叶斯网络进行军事工程毁伤评估与推理的有效性。     

On the combination of logical and probabilistic models for?information analysis

Formal logical tools are able to provide some amount of reasoning support for information analysis, but are unable to represent uncertainty. Bayesian network tools represent probabilistic and causal information, but in the worst case scale as poorly as some formal logical systems and require specialized expertise to use effectively. We describe a framework for systems that incorporate the advantages of both Bayesian and logical systems. We define a formalism for the conversion of automatically generated natural deduction proof trees into Bayesian networks. We then demonstrate that the merging of such networks with domain-specific causal models forms a consistent Bayesian network with correct values for the formulas derived in the proof. In particular, we show that hard evidential updates in which the premises of a proof are found to be true force the conclusions of the proof to be true with probability one, regardless of any dependencies and prior probability values assumed for the causal model. We provide several examples that demonstrate the generality of the natural deduction system by using inference schemes not supportable directly in Horn clause logic. We compare our approach to other ones, including some that use non-standard logics.     

Representing and processing lineages over uncertain data based on the Bayesian network

Processing lineages (also called provenances) over uncertain data consists in tracing the origin of uncertainty based on the process of data production and evolution. In this paper, we focus on the representation and processing of lineages over uncertain data, where we adopt Bayesian network (BN), one of the popular and important probabilistic graphical models (PGMs), as the framework of uncertainty representation and inferences. Starting from the lineage expressed as Boolean formulae for SPJ (Selection–Projection–Join) queries over uncertain data, we propose a method to transform the lineage expression into directed acyclic graphs (DAGs) equivalently. Specifically, we discuss the corresponding probabilistic semantics and properties to guarantee that the graphical model can support effective probabilistic inferences in lineage processing theoretically. Then, we propose the function-based method to compute the conditional probability table (CPT) for each node in the DAG. The BN for representing lineage expressions over uncertain data, called lineage BN and abbreviated as LBN, can be constructed while generally suitable for both safe and unsafe query plans. Therefore, we give the variable-elimination-based algorithm for LBN's exact inferences to obtain the probabilities of query results, called LBN-based query processing. Then, we focus on obtaining the probabilities of inputs or intermediate tuples conditioned on query results, called LBN-based inference query processing, and give the Gibbs-sampling-based algorithm for LBN's approximate inferences. Experimental results show the efficiency and effectiveness of our methods.     

A framework for the analysis of dynamic processes based on Bayesian networks and case-based reasoning

Bayesian networks are knowledge representation schemes that can capture probabilistic relationships among variables and perform probabilistic inference. Arrival of new evidence propagates through the network until all variables are updated. At the end of propagation, the network becomes a static snapshot representing the state of the domain for that particular time. This weakness in capturing temporal semantics has limited the use of Bayesian networks to domains in which time dependency is not a critical factor. This paper describes a framework that combines Bayesian networks and case-based reasoning to create a knowledge representation scheme capable of dealing with time-varying processes. Static Bayesian network topologies are learned from previously available raw data and from sets of constraints describing significant events. These constraints are defined as sets of variables assuming significant values. As new data are gathered, dynamic changes to the topology of a Bayesian network are assimilated using techniques that combine single-value decomposition and minimum distance length. The new topologies are capable of forecasting the occurrences of significant events given specific conditions and monitoring changes over time. Since environment problems are good examples of temporal variations, the problem of forecasting ozone levels in Mexico City was used to test this framework.     

Probabilistic temporal reasoning and its application to fossil power plant operation

Many real-world applications, such as industrial diagnosis, require an adequate representation and inference mechanism that combines uncertainty and time. In this work, we propose a novel approach for representing dynamic domains under uncertainty based on a probabilistic framework, called temporal nodes Bayesian networks (TNBN). The TNBN model is an extension of a standard Bayesian network, in which each temporal node represents an event or state change of a variable and the arcs represent causal–temporal relationships between nodes. A temporal node has associated a probability distribution for its time of occurrence, where time is discretized in a finite number of temporal intervals; allowing a different number of intervals for each node and a different duration for the intervals within a node (multiple granularity). The main difference with previous probabilistic temporal models is that the representation is based on state changes at different times instead of state values at different times. Given this model, we can reason about the probability of occurrence of certain events, for diagnosis or prediction, using standard probability propagation techniques developed for Bayesian networks. The proposed approach is applied to fossil power plant diagnosis through two detailed case studies: power load increment and control level system failure. The results show that the proposed formalism could help to improve power plant availability through early diagnosis of events and disturbances.     

贝叶斯网络在战术态势估计中的应用

战场态势估计是指挥决策的基础,如何进行合理的态势估计是当前战场指挥系统中最重要的组成部分;作为一种知识表示和进行概率推理的框架,贝叶斯网络在具有内在不确定性的推理和决策问题中得到了广泛的应用;因果推理是态势估计中的一个重要环节,用贝叶斯网络找出态势假设和事件之间的潜在关系,正是态势估计所需完成的功能;根据态势与事件之间不同的连接关系建立态势估计的贝叶斯网络模型,介绍贝叶斯网络推理算法和步骤,并给出实例仿真;结果表明,将贝叶斯网络用于态势估计,能够进行推理得到完整的战场态势信息,为决策提供依据。     

NAT model–based compression of Bayesian network CPTs over multivalued variables

Nonimpeding noisy‐AND tree (NAT) models offer a highly expressive approximate representation for significantly reducing the space of Bayesian networks (BNs). They also improve efficiency of BN inference significantly. To enable these advantages for general BNs, several technical advancements are made in this work to compress target BN conditional probability tables (CPTs) over multivalued variables into NAT models. We extend the semantics of NAT models beyond graded variables that causal independence models commonly adhered to and allow NAT modeling in nominal causal variables. We overcome the limitation of well‐defined pairwise causal interaction (PCI) bits and present a flexible PCI pattern extraction from target CPTs. We extend parameter estimation for binary NAT models to constrained gradient descent for compressing target CPTs over multivalued variables. We reveal challenges associated with persistent leaky causes and develop a novel framework for PCI pattern extraction when persistent leaky causes exist. The effectiveness of the CPT compression is validated experimentally.     

Modeling Causal Reinforcement and Undermining for Efficient CPT Elicitation

Representation of uncertain knowledge by using a Bayesian network requires the acquisition of a conditional probability table (CPT) for each variable. The CPT can be acquired by data mining or elicitation. When data are insufficient for supporting mining, causal modeling such as the noisy-OR aids elicitation by reducing the number of probability parameters to be acquired from human experts. Multiple causes can reinforce each other in producing the effect or can undermine the impact of each other. Most existing causal models do not consider causal interactions from the perspective of reinforcement or undermining. Our analysis shows that none can represent both interactions. Except for the RNOR, other models also limit parameters to probabilities of single-cause events. We present the first general causal model, that is, the nonimpeding noisy-AND tree, that allows encoding of both reinforcement and undermining. It supports efficient CPT acquisition by elicitating a partial ordering of causes in terms of a tree topology, plus the necessary numerical parameters. It also allows the incorporation of probabilities for multicause events.     

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.     

Research on the Application of Bayesian Network in Agriculture Intelligent System

Bayesian network is a strong tool for uncertain knowledge representation and inference. This paper mainly introduces some technologies and methods about Bayesian network based on intelligent system. In the construction of Bayesian network, divorcing technology and noisy-or technology are used. In the inference of Bayesian network, VE algorithm and sampling algorithm are introduced. Finally, Bayesian network construction component and inference component are developed. Then an expert system about cow disease diagnosis is constructed based on the two components.     

一种基于贝叶斯网络的作战重心评估模型

作战重心（Center of Gravity）是指战役体系中敌我双方的关键环节。作战重心评估是一个经验性、模糊性的过程。贝叶斯网络作为一种不确定知识表示模型,具有概率论及图论基础,对于解决复杂系统决策问题具有较强的优势,适合用于作战重心评估。文中提出并实现了一种基于贝叶斯网络推理的作战重心评估模型。通过该模型,可以定量地评估各个环节对于证据的重要程度,从而确定该作战过程中的作战重心。文中使用联合树（Clique Tree）算法进行贝叶斯网络精确推理,并详细阐述了推理过程中联合树建立,消息传递的过程。最后通过实例验证,基于贝叶斯网络推理的模型能够有效地对作战重心进行定量的评估。     

A Bayesian network-based framework for semantic image understanding

Current research in content-based semantic image understanding is largely confined to exemplar-based approaches built on low-level feature extraction and classification. The ability to extract both low-level and semantic features and perform knowledge integration of different types of features is expected to raise semantic image understanding to a new level. Belief networks, or Bayesian networks (BN), have proven to be an effective knowledge representation and inference engine in artificial intelligence and expert systems research. Their effectiveness is due to the ability to explicitly integrate domain knowledge in the network structure and to reduce a joint probability distribution to conditional independence relationships. In this paper, we present a general-purpose knowledge integration framework that employs BN in integrating both low-level and semantic features. The efficacy of this framework is demonstrated via three applications involving semantic understanding of pictorial images. The first application aims at detecting main photographic subjects in an image, the second aims at selecting the most appealing image in an event, and the third aims at classifying images into indoor or outdoor scenes. With these diverse examples, we demonstrate that effective inference engines can be built within this powerful and flexible framework according to specific domain knowledge and available training data to solve inherently uncertain vision problems.