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.     

ICIC_Target:目标节点的局部因果关系网络的发现算法

因果关系的研究在于揭示自然规律的和人类社会发展本质及其规律,对人类长久以来的生产生活和科学研究有着非常重要的作用.目前,因果关系的研究受到前所未有的广泛关注,但仍存在诸多困难和挑战.致力于建立一个因果激励抑制模型以抽象地表示和解释因果的作用机制,并在此基础上提出用于目标节点的局部因果关系网络的自动发现方法框架ICIC和算法ICIC_Target.该方法不预先设定因果结构(如设定为无圈、隐含结构),并根据对因果关系本质的认识,利用初始变量(exogenous variables)和初始团树(IClique)的概念,在判定边和方向之前对变量进行粗略地排序,从而提高了因果关系网络发现的性能.在4个不同类型的数据集上实现了与多种经典方法,如HITON,IC,PC,PCMB等的对比实验,实验结果表明ICIC_Target方法适用范围广,有较好的鲁棒性,同时,从理论上分析证实了ICIC_Target方法具有较好的稳定性和较低的复杂度.     

A new causal discovery heuristic

Probabilistic methods for causal discovery are based on the detection of patterns of correlation between variables. They are based on statistical theory and have revolutionised the study of causality. However, when correlation itself is unreliable, so are probabilistic methods: unusual data can lead to spurious causal links, while nonmonotonic functional relationships between variables can prevent the detection of causal links. We describe a new heuristic method for inferring causality between two continuous variables, based on randomness and unimodality tests and making few assumptions about the data. We evaluate the method against probabilistic and additive noise algorithms on real and artificial datasets, and show that it performs competitively.     

Probabilistic models considering dependent relation in reasoning for decision-making

This paper proposes a fuzzy dependence-index for construction of the probabilistic models considering dependent relation for solving the reasoning problem. It is important for constructing the joint probability-distribution to consider the dependency of events. We consider that some vagueness is included in the dependency. Because causal relationship of among events is uncertain, it is difficult to express dependency as definite value. In this paper, we classify the dependent relations, and apply the fuzzy probability to calculation of the dependence-index. Then, the fuzzy dependence-index is defined to consider dependency with fuzziness. Using the fuzzy dependence-index, we calculate the joint probability of multi-events for constructing the probabilistic model. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

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.     

Scalable Techniques for Mining Causal Structures

Mining for association rules in market basket data has proved a fruitful area of research. Measures such as conditional probability (confidence) and correlation have been used to infer rules of the form “the existence of item A implies the existence of item B.” However, such rules indicate only a statistical relationship between A and B. They do not specify the nature of the relationship: whether the presence of A causes the presence of B, or the converse, or some other attribute or phenomenon causes both to appear together. In applications, knowing such causal relationships is extremely useful for enhancing understanding and effecting change. While distinguishing causality from correlation is a truly difficult problem, recent work in statistics and Bayesian learning provide some avenues of attack. In these fields, the goal has generally been to learn complete causal models, which are essentially impossible to learn in large-scale data mining applications with a large number of variables. In this paper, we consider the problem of determining casual relationships, instead of mere associations, when mining market basket data. We identify some problems with the direct application of Bayesian learning ideas to mining large databases, concerning both the scalability of algorithms and the appropriateness of the statistical techniques, and introduce some initial ideas for dealing with these problems. We present experimental results from applying our algorithms on several large, real-world data sets. The results indicate that the approach proposed here is both computationally feasible and successful in identifying interesting causal structures. An interesting outcome is that it is perhaps easier to infer the lack of causality than to infer causality, information that is useful in preventing erroneous decision making.     

Logical clock requirements for reverse engineering scenarios from adistributed system

To reverse engineer scenarios from event traces, one must infer causal relationships between events. The inferences are usually based on a trace with sequence numbers or timestamps corresponding to some kind of logical clock. In practice, there is an explosion of potentially causal relationships in the trace, which limits one's ability to extract scenarios. This work defines a more parsimonious form of causality called scenario causality that concentrates on certain major causal relationships and ignores more subtle, potentially causal links. The influence of an event is restricted to the particular scenario it is part of. An event which is not a message reception is defined to be caused by the previous event in the same software object, while a message reception is caused by a sending event in another object. The events are ordered to form a scenario event graph where typed nodes are events and the typed edges are certain causal relationships. Intuitively, we might say that most logical clocks, which identify events which "happened before" a given event and, thus, are potentially causal, give an upper bound on the set of causal events; scenario causality identifies a lower bound. The much smaller lower bound set makes it possible to reverse engineer and automate the analysis of scenarios     

Animating Causal Overlays

Most approaches to representing causality, such as the common causal graph, require a separate and static view, but in many cases it is useful to add the dimension of causality to the context of an existing visualization. Building on research from perceptual psychology that shows the perception of causality is a low‐level visual event derived from certain types of motion, we are investigating how to add animated causal representations, called visual causal vectors, onto other visualizations. We refer to these as causal overlays. Our initial experimental results show this approach has great potential but that extra cues are needed to elicit the perception of causality when the motions are overlaid on other graphical objects. In this paper we describe the approach and report on a study that examined two issues of this technique: how to accurately convey the causal flow and how to represent the strength of the causal effect.     

向量自回归模型Granger因果图的条件互信息辨识与应用

Grangerl因果性是衡量系统变量间动态关系的重要依据．传统的两变量Grangerl因果分析法容易产生伪因果关系,且不能刻画变量间的即时因果性．本文利用图模型方法研究时间序列变量间的Grangerl因果关系,建立了时间序列Granger因果图,提出Grangerl因果图的条件互信息辨识方法,利用混沌理论中的关联积分估计条件互信息,统计量的显著性由置换检验确定．仿真结果证实了方法的有效性,并利用该方法研究了空气污染指标以及中国股市间的Grangerl因果关系．     

因果关系及其在社会媒体上的应用研究综述

诸如物理学、行为学、社会学和生物学中许多研究的中心问题是对因果的阐述,即变量或事件之间直接作用关系的阐述。由于人们的日常行为和语言越来越多地映射到互联网上,或者根本就是互联网引起了大量新的行为和语言,致使社会媒体上存在大量的因果问题。与相关关系分析相比,社会媒体上的因果关系分析更加必要和迫切,首先,任何相关性的背后都隐藏着因果关系;其次,相关性分析得到的结论有时是不可靠的甚至是错误的;再次,基于相关性的方法无法用于管理、控制和干预变量或事件。论述了因果关系分析的必要性、重要性和社会媒体上存在的因果问题;综述了目前的因果分析与推断的基本理论、存在的问题和研究现状;通过比较现有因果关系分析的研究思路,预测未来的研究方向和因果分析理论及方法在社会媒体上的应用。     

运用偏相关因果分析推断神经网络的真实结构

自从格兰杰提出因果关系的概念之后,格兰杰因果关系在构造神经网络的结构方面的应用越来越广泛,因为它可以得到神经网络的一个有向图。对于只有两个神经元的神经元网络,可以用通常的格兰杰因果关系去分析它们谁是因,谁是果。对于三个神经元以上的神经网络,由于神经元之间存在间接的作用,就不能象对两个神经元直接运用格兰杰因果关系去研究它们之间的结构了,而要用偏相关因果关系进行分析。论文介绍了偏相关因果关系的基本概念,并对一个模拟的三个神经元的网络比较了格兰杰因果关系和偏相关因果关系的区别。     

融合因果关系表征的阅读理解因果关系类选项判断

阅读理解因果关系类选项是指存在因果线索词的选项,此类选项需要根据原文中的因果关系表征进行作答。基于高考阅读理解任务构建因果关系网络,提出融合因果关系表征的因果关系类选项判断方法。采用模式匹配方法抽取原文的因果句对,根据文章因果句对抽取出因果关系词对,并通过点互信息计算因果关系词对之间的因果关联强度,从而构建因果关系网络来表征原文的因果关系。在此基础上,将因果关系表征融入到BERT模型中,预测因果关系选项和原文是否一致。同时,根据高考阅读理解大纲结合语料库发现错误类型分为因果颠倒、强加因果、偷换原因或结果、其他类型等4类,根据每一种错误类型的特点结合预测结果确定选项的错误类型,并提供一个错误解释,以增强方法的可解释性。选用近15年全国高考试题及模拟题中的4 071个科技类阅读理解因果选项进行实验,结果显示F1值达到62.09%,验证了该方法的有效性。     

频域格兰杰因果关系及其在信号处理中的应用

自从格兰杰1969年提出因果关系的概念之后,格兰杰因果关系在信号处理、计算神经科学等许多领域的应用越来越广。人们可以利用格兰杰因果关系来分析多个变量之间的直接的相互作用,从而进一步研究各类变量之间的内在联系。以往都是在时域空间进行分析的,也就是说分析的对象都是时间序列数据,研究这些变量之间随着时间的变化是如何联系的。在时域空间的基础上,进一步从频域空间上对变量进行研究,分析在哪个频率段上变量之间存在相互作用,所得到的结论当然更具有意义。     

Vector time and causality among abstract events in distributed computations

An important problem in analyzing distributed computations is the amount of information. In event-based models, even for simple applications, the number of events is large and the causal structure is complex. Event abstraction can be used to reduce the apparent complexity of a distributed computation. This paper discusses one important aspect of event abstraction: causality among abstract events. Following Lamport [24], two causality relations are defined on abstract events, called weak and strong precedence. A general theoretical framework based on logical vector time is developed in which several meaningful timestamps for abstract events are derived. These timestamps can be used to efficiently determine causal relationships between arbitrary abstract events. The class of convex abstract events is identified as a subclass of abstract events that is general enough to be widely applicable and restricted enough to simplify timestamping schemes used for characterizing weak precedence. We explain why such a simplification seems not possible for strong precedence. Received: February 1994 / Accepted: July 1997     

Causality analysis of neural connectivity: New tool and limitations of spectral Granger causality

Granger causality (GC) is one of the most popular measures to reveal causality influence of time series based on the estimated linear regression model and has been widely applied in economics and neuroscience due to its simplicity, understandability and easy implementation. Especially, its counterpart in frequency domain, spectral GC, has recently received growing attention to study causal interactions of neurophysiological data in different frequency ranges. In this paper, on the one hand, for one equality in the linear regression model (frequency domain) we point out that all items at the right-hand side of the equality make contributions (thus have causal influence) to the unique item at the left-hand side of the equality, and thus a reasonable definition for causality from one variable to another variable (i.e., the unique item) should be able to describe what percentage the variable occupies among all these contributions. Along this line, we propose a new spectral causality definition. On the other hand, we point out that spectral GC has its inherent limitations because of the use of the transfer function of the linear regression model and as a result may not reveal real causality at all and lead to misinterpretation result. By one example we demonstrate that the results of spectral GC analysis are misleading but the results from our definition are much reasonable. So, our new tool may have wide potential applications in neuroscience.     

Data integration with uncertainty

This paper reports our first set of results on managing uncertainty in data integration. We posit that data-integration systems need to handle uncertainty at three levels and do so in a principled fashion. First, the semantic mappings between the data sources and the mediated schema may be approximate because there may be too many of them to be created and maintained or because in some domains (e.g., bioinformatics) it is not clear what the mappings should be. Second, the data from the sources may be extracted using information extraction techniques and so may yield erroneous data. Third, queries to the system may be posed with keywords rather than in a structured form. As a first step to building such a system, we introduce the concept of probabilistic schema mappings and analyze their formal foundations. We show that there are two possible semantics for such mappings: by-table semantics assumes that there exists a correct mapping but we do not know what it is; by-tuple semantics assumes that the correct mapping may depend on the particular tuple in the source data. We present the query complexity and algorithms for answering queries in the presence of probabilistic schema mappings, and we describe an algorithm for efficiently computing the top-k answers to queries in such a setting. Finally, we consider using probabilistic mappings in the scenario of data exchange.     

基于简化因果图的工业过程故障根本变量诊断

在对工业过程故障进行根本原因诊断时,由于过程的自身特性和反馈控制等因素的干扰,使得变量因果图过于复杂从而使故障传播路径难以解释且不能找到导致故障的根本变量。提出一种简化因果图的方法,通过两步走对收敛交叉映射法构建的因果图实现简化,保留主要的故障传播路径。首先采用模糊综合评判法判别因果图中不确定性的关系;然后通过求解最大生成树,得到赋权无向图,并根据变量间因果关系选取根节点,分析赋权无向图获得新路径,从而将其改进成赋权有向图。在田纳西—伊斯曼过程进行验证实验,并与传统收敛交叉映射法进行比较,结果表明所提出方法的有效性。     

Resource-bounded measure on probabilistic classes

We extend Lutz's resource-bounded measure to probabilistic classes, and obtain notions of resource-bounded measure on probabilistic complexity classes such as BPE and BPEXP. Unlike former attempts, our resource bounded measure notions satisfy all three basic measure properties, that is every singleton {L} has measure zero, the whole space has measure one, and “enumerable infinite unions” of measure zero sets have measure zero.     

面向故障间格兰杰因果发现的霍克斯过程研究

现有因果关系建模方法应用于故障事件序列时,难以有效引入因果先验,使得算法结果过于稠密,同时在稀疏、时间精度低的数据上因果关系可靠性较差。将不同故障类型事件的因果关系建模为基于霍克斯过程的格兰杰因果关系,提出一种面向故障序列的格兰杰因果发现的霍克斯过程模型。将霍克斯过程拓展到离散时间域,解决低时间精度数据的建模问题,并通过构造基于贝叶斯信息准则的目标函数,保证因果结构稀疏性,进而利用基于EM算法与爬山法的迭代优化算法引入因果先验,提高模型的可靠性。实验结果表明,该方法在由不同参数生成的模拟数据上均表现突出,且在两个通信网络的真实数据集中,F1评分相比ADM4、MLE-SGL、TSSO和PCMCI算法提升15.18%以上。而通过引入根因标注和因果依赖性先验,算法的F1评分进一步提升22.43%以上,验证了引入先验的有效性。