Causality, conditional independence, and graphical separation in settable systems

We study the connections between causal relations and conditional independence within the settable systems extension of the Pearl causal model (PCM). Our analysis clearly distinguishes between causal notions and probabilistic notions, and it does not formally rely on graphical representations. As a foundation, we provide definitions in terms of suitable functional dependence for direct causality and for indirect and total causality via and exclusive of a set of variables. Based on these foundations, we provide causal and stochastic conditions formally characterizing conditional dependence among random vectors of interest in structural systems by stating and proving the conditional Reichenbach principle of common cause, obtaining the classical Reichenbach principle as a corollary. We apply the conditional Reichenbach principle to show that the useful tools of d-separation and D-separation can be employed to establish conditional independence within suitably restricted settable systems analogous to Markovian PCMs.     

A new approach toward modeling causality in commonsense reasoning

This article examines the issue of causality in commonsense reasoning and proposes a connectionist approach for modeling commonsense causal reasoning. Based on an analysis of the advantages and limitations of existing accounts, especially Shoham's logic, a generalized rule-based model FEL is proposed that can take into account the inexactness and the cumulative evidentiality of commonsense reasoning; this model corresponds naturally to a connectionist architecture. Detailed analyses are performed to show how the model handles commonsense causal reasoning. This work shows that a logic-based account of causality can be viewed as an (over)idealization of a more realistic model, which is simpler in form but deals with causality better. This work directly maps a (causal) rule-encoding scheme into a connectionist model; thus, it serves to link rule-based reasoning to connectionist models, notably with direct one-to-one correspondence between the basic structures of the two formalisms. © 1995 John Wiley & Sons, Inc.     

An Exploratory User Study of Visual Causality Analysis

Interactive visualization tools are being used by an increasing number of members of the general public; however, little is known about how, and how well, people use visualizations to infer causality. Adapted from the mediation causal model, we designed an analytic framework to systematically evaluate human performance, strategies, and pitfalls in a visual causal reasoning task. We recruited 24 participants and asked them to identify the mediators in a fictitious dataset using bar charts and scatter plots within our visualization interface. The results showed that the accuracy of their responses as to whether a variable is a mediator significantly decreased when a confounding variable directly influenced the variable being analyzed. Further analysis demonstrated how individual visualization exploration strategies and interfaces might influence reasoning performance. We also identified common strategies and pitfalls in their causal reasoning processes. Design implications for how future visual analytics tools can be designed to better support causal inference are discussed.     

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.     

Using default and causal reasoning in diagnosis

We present a theory of default reasoning that is specifically targeted to causal domains. These domains encompass a wide variety of current applications of default reasoning, but here we concentrate on model-based diagnosis. The theory is unique in that it integrates a formal notion of causality with nonmonotonic reasoning techniques based on default logic and abduction. The main structure of the theory is a default causal net (DCN) representing the causal connections among propositions in the domain. The causal net provides a framework for the two nonmonotonic reasoning techniques of assuming defaults and generating explanations for observations, allowing them to be combined in a principled way.     

Discovering causality in large databases

A causal rule between two variables, X M Y, captures the relationship that the presence of X causes the appearance of Y. Because of its usefulness (compared to association rules), techniques for mining causal rules are beginning to be developed. However, the effectiveness of existing methods (such as the LCD and CU-path algorithms) are limited to mining causal rules among simple variables, and are inadequate to discover and represent causal rules among multi-value variables. In this paper, we propose that the causality between variables X and Y be represented in the form X M Y with conditional probability matrix M Y|X . We also propose a new approach to discover causality in large databases based on partitioning. The approach partitions the items into item variables by decomposing "bad" item variables and composing "not-good" item variables. In particular, we establish a method to optimize causal rules that merges the "useless" information in conditional probability matrices of extracted causal rules.     

Complexity results for structure-based causality

We give a precise picture of the computational complexity of causal relationships in Pearl's structural models, where we focus on causality between variables, event causality, and probabilistic causality. As for causality between variables, we consider the notions of causal irrelevance, cause, cause in a context, direct cause, and indirect cause. As for event causality, we analyze the complexity of the notions of necessary and possible cause, and of the sophisticated notions of weak and actual cause by Halpern and Pearl. In the course of this, we also prove an open conjecture by Halpern and Pearl, and establish other semantic results. We then analyze the complexity of the probabilistic notions of probabilistic causal irrelevance, likely causes of events, and occurrences of events despite other events. Moreover, we consider decision and optimization problems involving counterfactual formulas. To our knowledge, no complexity aspects of causal relationships in the structural-model approach have been considered so far, and our results shed light on this issue.     

基于贝叶斯网络的时间序列因果关系学习

贝叶斯网络是研究变量之间因果关系的有力工具,基于贝叶斯网络的因果关系学习包括结构学习与参数学习两部分,其中,结构学习是核心.目前,贝叶斯网络主要用于发现非时间序列数据中所蕴含的因果关系（非时间序列因果关系）,从数据中学习得到的也均是一般变量之间的因果关系.针对这些情况,结合时间序列预处理、时间序列变量排序、转换数据集构建和局部贪婪打分-搜索等进行时间序列的因果关系学习;再将包括分段在内的时间序列预处理、时间序列段的因果关系结构学习、因果关系结构数据集构建、因果关系变量排序和局部贪婪打分-搜索等相结合,来进行元因果关系（因果关系变量之间的因果关系）学习,从而实现两个层次的时间序列因果关系学习,为进一步的量化因果分析奠定了基础.分别使用模拟、UCI和金融时间序列数据进行实验与分析,实验结果显示,基于贝叶斯网络能够有效地进行时间序列的因果关系和元因果关系学习.     

局部因果关系分析的隐变量发现算法

结构分析的隐变量发现方法难以有效地发现隐变量且可解释性较差。基于因果关系和局部结构的不确定性,提出了一种基于局部因果关系分析的隐变量发现算法（hidden variable discovering algorithm based on local causality analysis,LCAHD）。LCAHD算法给出了因果结构熵的定义,将因果知识和不确定性知识相融合,以因果关系的不确定性程度作为隐变量存在的判定依据,并对这一依据进行了理论上的论证。LCAHD算法首先通过寻找目标变量的马尔科夫毯来提取局部依赖结构,并基于扰动学习获得扰动数据,联合扰动数据和观测数据学习局部依赖结构中的因果关系;然后利用因果结构熵对局部因果结构中因果关系的不确定性进行度量,并利用隐变量和因果关系不确定性之间的相关性判定条件,确定隐变量的存在性。分别针对标准网络和股票网络进行了实验,结果表明,该算法能准确地确定隐变量的位置,具有较好的解释性。     

一种新颖的深度因果图建模及其故障诊断方法

为了实现复杂工业过程故障检测和诊断一体化建模, 提出了一种新颖的深度因果图建模方法. 首先, 利用循环神经网络建立深度因果图模型, 将Group Lasso稀疏惩罚项引入到模型训练中, 自动地检测过程变量间的因果关系. 其次, 利用模型学习到的条件概率预测模型对每个变量建立监测指标, 并融合得到综合指标进行整体工业过程故障检测. 一旦检测到故障, 对故障样本构建变量贡献度指标, 隔离故障相关变量, 并通过深度因果图模型的局部因果有向图诊断故障根源, 辨识故障传播路径. 最后, 通过田纳西?伊斯曼过程进行仿真验证, 实验结果验证了所提方法的有效性.     

复杂因果图并行推理算法研究

因果图的精确推理算法是NP难的,因此寻找高效的推理方法是值得研究的问题。介绍了因果关系研究进展,对经典因果图推理过程作了进一步分析,在此基础上提出了复杂因果图的并行推理算法,并对算法的时间复杂度进行了分析,最后用一个实例验证了算法的推理效果。研究表明,该复杂因果图并行推理算法有效地降低了时间复杂度,特别是在有环且处理机数量足够的情况下和无环且处理机有限的情况下,算法的复杂度是一个多项式时间复杂度,这为因果图提供了一种可行的新的推理方法。     

基于级联加性噪声模型的因果结构学习算法

现有级联非线性加性噪声模型可解决隐藏中间变量的因果方向推断问题,然而对于包含隐变量和级联传递因果关系的因果网络学习存在全局结构搜索、等价类无法识别等问题。设计一种面向非时序观测数据的两阶段因果结构学习算法,第一阶段根据观测数据变量间的条件独立性,构建基本的因果网络骨架,第二阶段基于级联非线性加性噪声模型,通过比较骨架中每个相邻因果对在不同因果方向假设下的边缘似然度进行因果方向推断。实验结果表明,该算法在虚拟因果结构数据集的不同隐变量数量、平均入度、结构维度、样本数量下均表现突出,且在真实因果结构数据集中的F1值相比主流因果结构学习算法平均提升了51%,具有更高的准确率和更强的鲁棒性。     

Identification of directed influence: Granger causality, Kullback-Leibler divergence, and complexity

Detecting and characterizing causal interdependencies and couplings between different activated brain areas from functional neuroimage time series measurements of their activity constitutes a significant step toward understanding the process of brain functions. In this letter, we make the simple point that all current statistics used to make inferences about directed influences in functional neuroimage time series are variants of the same underlying quantity. This includes directed transfer entropy, transinformation, Kullback-Leibler formulations, conditional mutual information, and Granger causality. Crucially, in the case of autoregressive modeling, the underlying quantity is the likelihood ratio that compares models with and without directed influences from the past when modeling the influence of one time series on another. This framework is also used to derive the relation between these measures of directed influence and the complexity or the order of directed influence. These results provide a framework for unifying the Kullback-Leibler divergence, Granger causality, and the complexity of directed influence.     

多值因果图的推理算法研究

针对多值因果图存在的两个困难：（1）不严格满足概率论；（2）将其用于实际问题时，推理结果可能出现错误，提出了一种基于因果影响可能性分配的推理算法，该算法将多值因果图的推量分成3个阶段，首先对多值因果图进行补充定义，使多值因果图能够兼容单值因果图；接着将多值因果图转化为单值因果图进行概率计算，最后对多值因果图进行可能性计算，将单值因果图计算得到的概率按多值因果图计算得到的可能性进行分配，以核电站二回路系统中蒸汽发生器故障诊断因果图为例，展示了该算法推理计算的全过程，实例表明，该算法能够有效地克服多值因果图存在的困难，其推理过程严谨，计算结果符合实际情况，而前面提出的推理算法基础上，针对其不能处理模型情况的局限性，提出了一种模糊推理算法，该算法对多值因果图进行了模糊扩展定义，在读数变量和事件变量之间建立了用于表达模糊知识的模糊对应关系，在事件变量上定义了一个等价的虚拟模糊状态，使读数变量取值对应一个模糊状态，把读数和模糊推理转化为对应模糊状态的非模糊推理，通过本文的工作，目前因果图已发展成了一个能够处理离散变量和连续变量的混合因果图模型。     

A neural network model of causality

This paper proposes a model for commonsense causal reasoning, based on the basic idea of neural networks. After an analysis of the advantages and limitations of existing accounts of causality, a fuzzy logic based formalism FEL is proposed that takes into account the inexactness and the cumulative evidentiality of commonsense causal reasoning, overcoming the limitations of existing accounts. Analyses concerning how FEL handles various aspects of commonsense causal reasoning are performed, in an abstract way. FEL can be implemented (naturally) in a neural (connectionist) network. This work also serves to link rule-based reasoning with neural network models, in that a rule-encoding scheme (FEL) is equated directly to a neural network model.     

Simplified Granger causality map for data-driven root cause diagnosis of process disturbances

Root cause diagnosis is an important step in process monitoring, which aims to identify the sources of process disturbances. The primary challenge is that process disturbances propagate between different operating units because of the flow of material and information. Data-driven causality analysis techniques, such as Granger causality (GC) test, have been widely adopted to construct process causal maps for root cause diagnosis. However, the generated causal map is over-complicated and difficult to interpret because of the existence of process loops and the violation of statistical assumptions. In this work, a two-step procedure is proposed to solve this problem. First, a causal map is built by adopting the conditional GC analysis, which is viewed as a graph in the next step. In this graph, each vertex corresponds to a process variable under investigation, while the weight of the edge connecting two vertices is the F-value calculated by conditional GC. This graph is then simplified by computing its maximum spanning tree. Thus, the results of the causality analysis are transformed into a directed acyclic graph, which eliminates all loops, highlights the root cause variable, and facilitates the diagnosis. The feasibility of this method is illustrated with the application to the Tennessee Eastman benchmark process. In the investigated case studies, the proposed method outperforms the conditional GC test and provides an easy way to identify the root cause of process disturbances.     

面向社交媒体的直接因果网络发现算法

高维时序因果网络发现是社交媒体因果关系发现的重要问题。然而,现有的时序因果关系发现方法不能发现直接因果以致因果网络推断结果不准确。针对此问题提出了一种直接因果网络发现方法。该方法考虑了时序因果模型的因果延迟、滞后期数量和条件节点集等因素,更准确地发现直接因果关系;另外,采用结合置换检验的因果关系检验方法,解决传递熵阈值难以设定的问题。实验结果表明,该方法在因果网络推断中优于现有方法,有效提升时序上直接因果网络推断的准确率,适用于发现潜在社交媒体因果关系网络。     

A study of patent analysis of LED bicycle light by using modified DEMATEL and life span

The present study proposed a modified decision-making trial and evaluation laboratory (DEMATEL) method. This innovation method involves collecting the repeated or identically defined technical keywords of patent techniques related to light-emitting diode (LED) bicycle light to determine the ratios of the normalized numerical values of these technical keywords by using one technical domain as the primary domain and another as a variable. The values obtained are then converted to mutual influence levels on a scale of 0 to 4, replacing the conventional expert questionnaire. In this study, in accordance with the operational steps of the decision-making trial and evaluation laboratory method, a general relational influence matrix, direct and indirect relationships diagram, and values of centrality (D + R) and causality (D − R) were obtained. A causal diagram was therefore created. The causal diagram was drawn using values of (D + R) and (D − R) as the two axes and facilitated determining the levels of mutual influence between technical domains. In accordance with the proposed modified decision-making trial and evaluation laboratory method, this study collected patents related to LED bicycle light; moreover, the normalized numerical values of key technical, part/component, and function words that appeared in these patents were calculated. Furthermore, clusters of technical and part or component words were defined in accordance with the first-layer technical category. The second-layer technical categories and functional categories were subsequently defined under the first-layer technical categories to establish the technique–function matrix, thereby dividing the techniques related to LED bicycle light into seven main technical domains. This study then analyzed patent life span. Patent life span was calculated using the announcement date of related patents. Finally, this study investigated the development potential of each technical domain of LED bicycle light by conducting a combined analysis of causal diagram obtained by modified DEMATEL method, activity trend chart of techniques, and patent life spans. The proposed patent analysis method and results can serve companies and engineers as references to facilitate developing new patents.     

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...