Sensitivity analysis on causal chains of Bayesian networks

To analyze the key path of Bayesian network in complex systems, this study proposes to analyze the sensitivity of causal chains of Bayesian networks using the Petri net structural analysis approach to obtain the key chain through which the cause influences the consequence. First, the Bayesian network is transformed into Petri net, the structural analysis approach of which is employed to analyze structural nature of the Bayesian network, ensuring correctness of the constructed Bayesian network structure. Then based on the above fact that the structure is correct, S‐invariants of a Petri net is used to search for simple causal chains of the Bayesian network. Finally, the causal effect is defined and sensitivity analysis is made on the causal chains. The said method is applied to MDS causal chain analysis. Results show that the proposed method is direct viewing and practical. This method has some reference value for decision making in complex systems. © 2011 Wiley Periodicals, Inc.     

Learning Bayesian networks for discrete data

Bayesian networks have received much attention in the recent literature. In this article, we propose an approach to learn Bayesian networks using the stochastic approximation Monte Carlo (SAMC) algorithm. Our approach has two nice features. Firstly, it possesses the self-adjusting mechanism and thus avoids essentially the local-trap problem suffered by conventional MCMC simulation-based approaches in learning Bayesian networks. Secondly, it falls into the class of dynamic importance sampling algorithms; the network features can be inferred by dynamically weighted averaging the samples generated in the learning process, and the resulting estimates can have much lower variation than the single model-based estimates. The numerical results indicate that our approach can mix much faster over the space of Bayesian networks than the conventional MCMC simulation-based approaches.     

Inference in hybrid Bayesian networks with large discrete and continuous domains

Inference in Bayesian networks with large domain of discrete variables requires significant computational effort. In order to reduce the computational effort, current approaches often assume that discrete variables have some bounded number of values or are represented at an appropriate size of clusters. In this paper, we introduce decision-tree structured conditional probability representations that can efficiently handle a large domain of discrete and continuous variables. These representations can partition the large number of values into some reasonable number of clusters and lead to more robust parameter estimation. Very rapid computation and ability to treat both discrete and continuous variables are accomplished via modified belief propagation algorithm. Being able to compute various types of reasoning from a single Bayesian network eliminates development and maintenance issues associated with the use of distinct models for different types of reasoning. Application to real-world steel production process data is presented.     

Sensitivity analysis of discrete Kalman filters

This paper investigates the sensitivity of discrete Kalman filters to erroneous models. Both parameter and structure (state dimensionality) sensitivity are considered, as well as deterministic and random parameter errors. Iterative algorithms are derived for the calculation of the actual filter error covariance matrix for the case of known (deterministic) modelling errors. For the case of random statistical and dynamical modelling errors, an optimal mean-square error estimate of the actual system performance is derived.     

贝叶斯网络在学生模型建模中的应用分析

将课程教学资源融合到学生模型构建中,描述了包括领域知识拓扑结构的建立、条件概率表学习算法的推理的详细过程,最终得到了学生模型中关于章节知识项的贝叶斯网络结构图,并通过一个实验系统对个性化教学系统中学生模型建构的整个框架的可行性进行了验证.     

Comparative analysis of discretization methods in Bayesian networks

A key step in implementing Bayesian networks (BNs) is the discretization of continuous variables. There are several mathematical methods for constructing discrete distributions, the implications of which on the resulting model has not been discussed in literature. Discretization invariably results in loss of information, and both the discretization method and the number of intervals determines the level of such loss. We designed an experiment to evaluate the impact of commonly used discretization methods and number of intervals on the developed BNs. The conditional probability tables, model predictions, and management recommendations were compared and shown to be different among models. However, none of the models did uniformly well in all comparison criteria. As we cannot justify using one discretization method against others, we recommend caution when discretization is used, and a verification process that includes evaluating alternative methods to ensure that the conclusions are not an artifact of the discretization approach.     

A heuristic method for learning Bayesian networks using discrete particle swarm optimization

Bayesian networks are a powerful approach for representing and reasoning under conditions of uncertainty. Many researchers aim to find good algorithms for learning Bayesian networks from data. And the heuristic search algorithm is one of the most effective algorithms. Because the number of possible structures grows exponentially with the number of variables, learning the model structure from data by considering all possible structures exhaustively is infeasible. PSO (particle swarm optimization), a powerful optimal heuristic search algorithm, has been applied in various fields. Unfortunately, the classical PSO algorithm only operates in continuous and real-valued space, and the problem of Bayesian networks learning is in discrete space. In this paper, two modifications of updating rules for velocity and position are introduced and a Bayesian networks learning based on binary PSO is proposed. Experimental results show that it is more efficient because only fewer generations are needed to obtain optimal Bayesian networks structures. In the comparison, this method outperforms other heuristic methods such as GA (genetic algorithm) and classical binary PSO.     

Bayesian MLP neural networks for image analysis

We demonstrate the advantages of using Bayesian multi-layer perceptron (MLP) neural networks for image analysis. The Bayesian approach provides consistent way to do inference by combining the evidence from the data to prior knowledge from the problem. A practical problem with MLPs is to select the correct complexity for the model, i.e., the right number of hidden units or correct regularization parameters. The Bayesian approach offers efficient tools for avoiding overfitting even with very complex models, and facilitates estimation of the confidence intervals of the results. In this contribution we review the Bayesian methods for MLPs and present comparison results from two case studies. In the first case, MLPs were used to solve the inverse problem in electrical impedance tomography. The Bayesian MLP provided consistently better results than other methods. In the second case, the goal was to locate trunks of trees in forest scenes. With Bayesian MLP it was possible to use large number of potentially useful features and prior for determining the relevance of the features automatically.     

基于贝叶斯网络的系统可靠性分析平台

贝叶斯网络是一种进行不确定性推理和分析的有效工具,针对系统可靠性分析问题,建立了一种基于贝叶斯网络的系统可靠性分析平台。所建立的分析平台将贝叶斯网络应用于系统可靠性分析中,把系统各组部件抽象成节点,从而构成贝叶斯网络模型;通过推理和分析算法找到影响系统可靠性的薄弱环节;通过计算某个部件发生变化时对整个系统的影响,得出各个节点的重要度,给出合理的优化方案,提升系统可靠性。通过对平视显示器实例进行分析,计算了每个组部件对整个系统的影响程度,证明该分析平台在利用贝叶斯网络对系统可靠性分析上的可行性。     

基于模糊贝叶斯网的危害性分析方法

针对传统的故障模式、影响与危害性分析(FMECA)方法不足的问题,提出了一个基于模糊贝叶斯网的危害性分析方法。该方法将模糊理论与贝叶斯网推理技术结合起来,用三角模糊数来描述专家的模糊评分值;通过模糊集合映射,将其转化为评级的模糊子集;以置信结构的模糊规则,表示故障模式的属性与危害度之间的关系;利用贝叶斯网络推理算法综合置信结构的模糊规则,通过贝叶斯网推理得到模糊子集形式的危害度,再经过去模糊计算,得到故障危害等级的清晰值,从而确定故障模式的危害程度。实验结果表明,所提方法能够提高传统分析方法的准确性和应用范围。     

Competitiveness analysis of automotive industry in Turkey using Bayesian networks

The purpose of this study is to analyze the relations between the factors that enable national competitive advantage and the establishment of competitive superiority in automotive industry through a comprehensive analytical model. Bayesian networks (BN) are used to investigate the associations of different factors in the automotive industry which lead to competitive advantage. The results of the study focus on building a road map for the automotive sector policy makers in their way to improve the competitiveness through scenario analysis. Using the probabilistic dependency structure of the Bayesian network all of the variables in the model can be estimated. Thus, with the proposed model the automotive industry can be analyzed as a whole system and not only in terms of single variables. Findings of the model indicate that technological developments in automotive industry can alter the nature of competition in this industry.     

Consistency of discrete Bayesian learning

Bayes’ rule specifies how to obtain a posterior from a class of hypotheses endowed with a prior and the observed data. There are three fundamental ways to use this posterior for predicting the future: marginalization (integration over the hypotheses w.r.t. the posterior), MAP (taking the a posteriori most probable hypothesis), and stochastic model selection (selecting a hypothesis at random according to the posterior distribution). If the hypothesis class is countable, and contains the data generating distribution (this is termed the “realizable case”), strong consistency theorems are known for the former two methods in a sequential prediction framework, asserting almost sure convergence of the predictions to the truth as well as loss bounds. We prove corresponding results for stochastic model selection, for both discrete and continuous observation spaces. As a main technical tool, we will use the concept of a potential: this quantity, which is always positive, measures the total possible amount of future prediction errors. Precisely, in each time step, the expected potential decrease upper bounds the expected error. We introduce the entropy potential of a hypothesis class as its worst-case entropy, with regard to the true distribution. Our results are proven within a general stochastic online prediction framework, that comprises both online classification and prediction of non-i.i.d. sequences.     

连续航班延误与波及的贝叶斯网络分析

针对空运系统日益严重的航班延误,尝试将贝叶斯方法应用于航班数据分析,重点考虑同一飞机飞行连续航班的情况。借助Netica软件包,建立贝叶斯网络模型。通过贝叶斯网络推理进行连续航班延误波及分析,并用实际航班数据进行测试。结果表明,概率统计意义下,模型能够清晰反映连续航班延误原因分布、过站时间差分布和按时间段的延误波及情况。     

Sensitivity analysis of distributed parameter elements in high-speed circuit networks

This paper presents an analysis method, based on MacCormack's technique, for the evaluation of the time domain sensitivity of distributed parameter elements in high-speed circuit networks. Sensitivities can be calculated from electrical and physical parameters of the distributed parameter elements. The proposed method is a direct numerical method of time-space discretization and does not require complicated mathematical deductive process. Therefore, it is very convenient to program this method. It can be applied to sensitivity analysis of general transmission lines in linear or nonlinear circuit networks. The proposed method is second-order-accurate. Numerical experiment is presented to demonstrate its accuracy and efficiency.     

Sensitivity analysis of distributed parameter elements in high-speed circuit networks

This paper presents an analysis method, based on MacCormack＇s technique, for the evaluation of the time domain sensitivity of distributed parameter elements in high-speed circuit networks. Sensitivities can be calculated from electrical and physical parameters of the distributed parameter elements. The proposed method is a direct numerical method of time-space discretization and does not require complicated mathematical deductive process. Therefore, it is very convenient to program this method. It can be applied to sensitivity analysis of general transmission lines in linear or nonlinear circuit networks. The proposed method is second-order-accurate. Numerical experiment is presented to demonstrate its accuracy and efficiency.     

Explaining inferences in Bayesian networks

While Bayesian network (BN) can achieve accurate predictions even with erroneous or incomplete evidence, explaining the inferences remains a challenge. Existing approaches fall short because they do not exploit variable interactions and cannot account for compensations during inferences. This paper proposes the Explaining BN Inferences (EBI) procedure for explaining how variables interact to reach conclusions. EBI explains the value of a target node in terms of the influential nodes in the target’s Markov blanket under specific contexts, where the Markov nodes include the target’s parents, children, and the children’s other parents. Working back from the target node, EBI shows the derivation of each intermediate variable, and finally explains how missing and erroneous evidence values are compensated. We validated EBI on a variety of problem domains, including mushroom classification, water purification and web page recommendation. The experiments show that EBI generates high quality, concise and comprehensible explanations for BN inferences, in particular the underlying compensation mechanism that enables BN to outperform alternative prediction systems, such as decision tree.     

Employing hierarchical Bayesian networks in simple and complex emotion topic analysis

Traditional emotion models, when tagging single emotions in documents, often ignore the fact that most documents convey complex human emotions. In this paper, we join emotion analysis with topic models to find complex emotions in documents, as well as the intensity of the emotions, and study how the document emotions vary with topics. Hierarchical Bayesian networks are employed to generate the latent topic variables and emotion variables. On average, our model on single emotion classification outperforms the traditional supervised machine learning models such as SVM and Naive Bayes. The other model on the complex emotion classification also achieves promising results. We thoroughly analyze the impact of vocabulary quality and topic quantity to emotion and intensity prediction in our experiments. The distribution of topics such as Friend and Job are found to be sensitive to the documents’ emotions, which we call emotion topic variation in this paper. This reveals the deeper relationship between topics and emotions.     

Using Bayesian networks for root cause analysis in statistical process control

Despite their fame and capability in detecting out-of-control conditions, control charts are not effective tools for fault diagnosis. There are other techniques in the literature mainly based on process information and control charts patterns to help control charts for root cause analysis. However these methods are limited in practice due to their dependency on the expertise of practitioners. In this study, we develop a network for capturing the cause and effect relationship among chart patterns, process information and possible root causes/assignable causes. This network is then trained under the framework of Bayesian networks and a suggested data structure using process information and chart patterns. The proposed method provides a real time identification of single and multiple assignable causes of failures as well as false alarms while improving itself performance by learning from mistakes. It also has an acceptable performance on missing data. This is demonstrated by comparing the performance of the proposed method with methods like neural nets and K-Nearest Neighbor under extensive simulation studies.     

Sensitivity analysis of single hidden-layer neural networks withthreshold functions

An important consideration when applying neural networks to pattern recognition is the sensitivity to weight perturbation or to input errors. In this paper, we analyze the sensitivity of single hidden-layer networks with threshold functions. In a case of weight perturbation or input errors, the probability of inversion error for an output neuron is derived as a function of the trained weights, the input pattern, and the variance of weight perturbation or the bit error probability of the input pattern. The derived results are verified with a simulation of the Madaline recognizing handwritten digits. The result shows that the sensitivity of trained networks is far different from that of networks with random weights.