基于约束学习的观测数据因果关系发现研究
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摘要
人类对自然的探索活动本质上是发现各种现象的原因,因果关系能够给出各种现象的解释,而这些解释能帮助我们理解和掌握自然规律。设计良好的实验研究是获得因果关系的最有效的方法,但是实验研究容易受伦理道德、实验代价等因素的限制而无法开展。随着数据收集和存储技术的快速发展,在工程、医疗和科学实验等领域每天都产生不可计量的观测数据。在随机实验方法无法开展时,可以转向基于观测数据的因果发现。基于观测数据的因果发现方法即是利用科学的理论和方法,揭示了蕴含在海量的观测数据中的因果关系。
从观测数据中发现因果关系具有非常重要的意义,同时也面临着许多实际的困难。因果关系没有普遍被接受的定义,不同的领域中的因果关系有不同的解释,很难使用统一的形式表达因果关系。在数据因果充分的条件下因果图模型给出了观测数据中对应的因果关系的直观表示。然而当数据因果充分条件在所有观测变量下不满足时往往不能构造正确的因果图。同时对观测数据中的变量构建因果图模型的效率与变量的数量成指数关系,随着变量数量的增加,全局因果图模型的约束学习代价将变的非常高。在实际的应用背景下,用户可能并不需要了解整个观测数据中包含的所有因果关系,发现其中一部分感兴趣的因果关系具有更大的理论意义和实现价值。为了解决现有因果模型学习和利用效率不高的问题,本文以研究观测数据因果关系发现为基础,针对观测数据的变量的一个子集学习对应的模型,通过获得的模型来表达和推导直接因果关系。论文的主要研究内容如下：
1.从因果关系理论出发,研究了不同的因果关系约束学习方法,针对现有因果关系约束方法需要大量条件独立性计算的问题,提出了因果关系一致性约束方法,通过融合目标变量在不同控制变量条件下的条件关联来实现变量约束,避免了大量条件独立计算。在一致性约束思想的基础上,提出了基于观测数据等价类的因果关系一致性约束方法,方法改进了观测数据中变量一致性约束策略,有效地降低了观测数据一致性约束实现的代价。对直接因果关系进行了明确的定义,并综合缺省逻辑和一阶谓词的特点,利用缺省逻辑的蕴含式扩展将直接因果关系用因果规则的形式进行表达,为变量的直接因果关系提供了一个简洁的语法和形式化表达的工具,并在因果规则的基础上构建了因果预测和因果诊断的模型。
2.因果规则是直接因果关系的有效表达形式,利用直接因果关系的理论从海量的观测数据中发现实际的因果规则具有重大的现实意义。针对传统关联规则兴趣度评价方法的不足,将因果关系引入关联规则兴趣度评价,基于信息量提出了一种因果规则度量方法。方法将不同关联规则之间的关系作为先验知识来剔除虚假和错误的因果规则,以兴趣度评价的方式实现了直接因果关系发现；同时提出了相应的算法,并通过实际数据比较和分析了该算法的性能。在关联规则的基础上进行直接因果关系发现能充分了关联规则挖掘的技术,为海量观测数据的直接因果关系发现提供了有益的探索。
3.针对基于因果贝叶斯网络的因果关系发现具有复杂度高、计算难度大等缺点,在直接因果关系的形式化表达基础上,构建了一个通用的直接因果关系发现框架。框架基于变量一致性约束的思想,利用关联和部分关联的分层约束实现直接因果关系的发现。同时框架将单一因素的直接因果关系发现扩展到组合变量的直接因果关系,解决了传统因果发现方法无法表示组合因果关系的问题。基于框架提出了一个高效的因果规则挖掘算法,设计了顺序等价类存储表和局部顺序等价类存储表,结合有效的数据表示和搜索空间剪枝技术,提高了发现因果规则的效率。通过充分的实验评估,算法在不同的数据集合中都实现了较好的性能表现,相对于传统的因果关系发现算法不仅提高了效率,并且在不同的数据集上具有良好的扩展性。
因果关系发现是知识发现领域的一个重要的课题,本文从观测数据的角度研究了直接因果关系的约束方法,讨论了因果规则的表达和推理形式,对海量观测数据的直接因果关系挖掘进行了探索,对数据挖掘领域中利用观测数据进行因果关系发现的理论研究和具体实践具有重要意义。
The essence of human exploration of natural is to find the cause of a variety of phenomena, which can be used to explain various phenomena and help us to understand and master the laws of nature. A well-designed randomized controlled experiment is the most effective way to identify causality, which however may be infeasible to be conducted for restrictions of cost and ethics. Massive amounts of observational data have being generated from all kinds of areas with the fast development of data collection and storage technology, such as engineering, medical and scientific. People can turn to discover causal relationship based on observational data using these methods when the random experimental method cannot be carried out. The causal discovery methods based on observational data are designed to reveal the causality embedded on the vast data.
It is very important and challenging to discover causal relationships from large databases of observational data. There is no generally acceptable definition for causal relationships, which may have different meanings in different areas, making it difficult to be expounded in a unified form. Causal Bayesian network is an important causal model, which can visually represent the causality embedded in observational data under causal sufficiency condition. However, an ideal causal graph usually cannot be constructed without causal sufficiency condition hold in all the observed variables. In addition, the cost of learning a causal Bayesian network exponentially increases with the number of variables, making the learning of a full causal Bayesian network infeasible with large number of variables. In practical, people may not interest to know all the causal relationship among the variables, therefore finding causal structures on a subset of the variables shows much greater significance. To address the problem in learning and using of current causal models, this dissertation aims to learn causal relationships from a subset of the variables underlies the big content of causal discovery from observational data. The major content of this dissertation are as follows:
1. This dissertation studies various constrain-based methods for causal discovery, and proposes a new method based on persistent constrain for the calculation of a large number of conditional independence in current constrain-based methods. The method integrates the partial association of a variable under distinct covariates, which avoiding to measuring the conditional independence. On the basis of persistent constrain, an improved method based on equivalence class is proposed, which effectively reduce the cost of conducting the persistent constrain. A formal definition of direct causal relationship is given, and formalized using causal rules based on extended default logic. It provides concise syntax and formal expression for direct causal relationship, and can be applied to structure models for causal prediction and causal diagnosis.
2. It is of great practical significance to find causal rules from observational data based on the foundational theory of direct causal relationship, since causal rules are effective expression of direct causal relationship. Causality is introduced into the interestingness measure of association rules and a new method for evaluating the causal rules using information entropy is proposed for the shortcomings and deficiencies of traditional interestingness measures. The interaction of different association rules are considered as prior knowledge to eliminate false and fake causal rule and find real causal rules using the interestingness measure. An algorithm is implemented on a real data and shows efficiency in mining causal rules from association rules. Causal rules discovery based on association rule provides a feasible solution to find causal relationship from observational data by taking full advantage of techniques in associate rule mining.
3. As the causal Bayesian network is too complex and difficult to learn and infer the causality, this dissertation presents a general framework for direct causal relationship discovery based on formalized causal rules. With layered means, the framework applies positive association and zero partial association to determine the causal rules, which sticking to the thought of persistent constrain. Causal relationship of single variables is extended to combined case, which has not been solved in traditional causal discovery methods. An efficient algorithm is presented according to the framework, and it improves the efficiency of mining causal rules using a well designed ordinal equivalence storage table and ordinal local equivalence storage table, as well some pruning technology. Through numerous experiments, the algorithm shows well performance and improves the efficiency of causal rules mining in relative to current methods.
Causality discovery is one of the most important topics in the field of knowledge discovery. Constrain-based methods for causal relationship from the perspective of observational data are studied in this dissertation, the formalization and inference of causal rules are discussed, and the practical mining of direct causal relationship from massive observational databases are explored. Those systematic works may be helpful for the research of theory and practice on causal discovery from observational data.
从观测数据中发现因果关系具有非常重要的意义,同时也面临着许多实际的困难。因果关系没有普遍被接受的定义,不同的领域中的因果关系有不同的解释,很难使用统一的形式表达因果关系。在数据因果充分的条件下因果图模型给出了观测数据中对应的因果关系的直观表示。然而当数据因果充分条件在所有观测变量下不满足时往往不能构造正确的因果图。同时对观测数据中的变量构建因果图模型的效率与变量的数量成指数关系,随着变量数量的增加,全局因果图模型的约束学习代价将变的非常高。在实际的应用背景下,用户可能并不需要了解整个观测数据中包含的所有因果关系,发现其中一部分感兴趣的因果关系具有更大的理论意义和实现价值。为了解决现有因果模型学习和利用效率不高的问题,本文以研究观测数据因果关系发现为基础,针对观测数据的变量的一个子集学习对应的模型,通过获得的模型来表达和推导直接因果关系。论文的主要研究内容如下：
1.从因果关系理论出发,研究了不同的因果关系约束学习方法,针对现有因果关系约束方法需要大量条件独立性计算的问题,提出了因果关系一致性约束方法,通过融合目标变量在不同控制变量条件下的条件关联来实现变量约束,避免了大量条件独立计算。在一致性约束思想的基础上,提出了基于观测数据等价类的因果关系一致性约束方法,方法改进了观测数据中变量一致性约束策略,有效地降低了观测数据一致性约束实现的代价。对直接因果关系进行了明确的定义,并综合缺省逻辑和一阶谓词的特点,利用缺省逻辑的蕴含式扩展将直接因果关系用因果规则的形式进行表达,为变量的直接因果关系提供了一个简洁的语法和形式化表达的工具,并在因果规则的基础上构建了因果预测和因果诊断的模型。
2.因果规则是直接因果关系的有效表达形式,利用直接因果关系的理论从海量的观测数据中发现实际的因果规则具有重大的现实意义。针对传统关联规则兴趣度评价方法的不足,将因果关系引入关联规则兴趣度评价,基于信息量提出了一种因果规则度量方法。方法将不同关联规则之间的关系作为先验知识来剔除虚假和错误的因果规则,以兴趣度评价的方式实现了直接因果关系发现；同时提出了相应的算法,并通过实际数据比较和分析了该算法的性能。在关联规则的基础上进行直接因果关系发现能充分了关联规则挖掘的技术,为海量观测数据的直接因果关系发现提供了有益的探索。
3.针对基于因果贝叶斯网络的因果关系发现具有复杂度高、计算难度大等缺点,在直接因果关系的形式化表达基础上,构建了一个通用的直接因果关系发现框架。框架基于变量一致性约束的思想,利用关联和部分关联的分层约束实现直接因果关系的发现。同时框架将单一因素的直接因果关系发现扩展到组合变量的直接因果关系,解决了传统因果发现方法无法表示组合因果关系的问题。基于框架提出了一个高效的因果规则挖掘算法,设计了顺序等价类存储表和局部顺序等价类存储表,结合有效的数据表示和搜索空间剪枝技术,提高了发现因果规则的效率。通过充分的实验评估,算法在不同的数据集合中都实现了较好的性能表现,相对于传统的因果关系发现算法不仅提高了效率,并且在不同的数据集上具有良好的扩展性。
因果关系发现是知识发现领域的一个重要的课题,本文从观测数据的角度研究了直接因果关系的约束方法,讨论了因果规则的表达和推理形式,对海量观测数据的直接因果关系挖掘进行了探索,对数据挖掘领域中利用观测数据进行因果关系发现的理论研究和具体实践具有重要意义。
The essence of human exploration of natural is to find the cause of a variety of phenomena, which can be used to explain various phenomena and help us to understand and master the laws of nature. A well-designed randomized controlled experiment is the most effective way to identify causality, which however may be infeasible to be conducted for restrictions of cost and ethics. Massive amounts of observational data have being generated from all kinds of areas with the fast development of data collection and storage technology, such as engineering, medical and scientific. People can turn to discover causal relationship based on observational data using these methods when the random experimental method cannot be carried out. The causal discovery methods based on observational data are designed to reveal the causality embedded on the vast data.
It is very important and challenging to discover causal relationships from large databases of observational data. There is no generally acceptable definition for causal relationships, which may have different meanings in different areas, making it difficult to be expounded in a unified form. Causal Bayesian network is an important causal model, which can visually represent the causality embedded in observational data under causal sufficiency condition. However, an ideal causal graph usually cannot be constructed without causal sufficiency condition hold in all the observed variables. In addition, the cost of learning a causal Bayesian network exponentially increases with the number of variables, making the learning of a full causal Bayesian network infeasible with large number of variables. In practical, people may not interest to know all the causal relationship among the variables, therefore finding causal structures on a subset of the variables shows much greater significance. To address the problem in learning and using of current causal models, this dissertation aims to learn causal relationships from a subset of the variables underlies the big content of causal discovery from observational data. The major content of this dissertation are as follows:
1. This dissertation studies various constrain-based methods for causal discovery, and proposes a new method based on persistent constrain for the calculation of a large number of conditional independence in current constrain-based methods. The method integrates the partial association of a variable under distinct covariates, which avoiding to measuring the conditional independence. On the basis of persistent constrain, an improved method based on equivalence class is proposed, which effectively reduce the cost of conducting the persistent constrain. A formal definition of direct causal relationship is given, and formalized using causal rules based on extended default logic. It provides concise syntax and formal expression for direct causal relationship, and can be applied to structure models for causal prediction and causal diagnosis.
2. It is of great practical significance to find causal rules from observational data based on the foundational theory of direct causal relationship, since causal rules are effective expression of direct causal relationship. Causality is introduced into the interestingness measure of association rules and a new method for evaluating the causal rules using information entropy is proposed for the shortcomings and deficiencies of traditional interestingness measures. The interaction of different association rules are considered as prior knowledge to eliminate false and fake causal rule and find real causal rules using the interestingness measure. An algorithm is implemented on a real data and shows efficiency in mining causal rules from association rules. Causal rules discovery based on association rule provides a feasible solution to find causal relationship from observational data by taking full advantage of techniques in associate rule mining.
3. As the causal Bayesian network is too complex and difficult to learn and infer the causality, this dissertation presents a general framework for direct causal relationship discovery based on formalized causal rules. With layered means, the framework applies positive association and zero partial association to determine the causal rules, which sticking to the thought of persistent constrain. Causal relationship of single variables is extended to combined case, which has not been solved in traditional causal discovery methods. An efficient algorithm is presented according to the framework, and it improves the efficiency of mining causal rules using a well designed ordinal equivalence storage table and ordinal local equivalence storage table, as well some pruning technology. Through numerous experiments, the algorithm shows well performance and improves the efficiency of causal rules mining in relative to current methods.
Causality discovery is one of the most important topics in the field of knowledge discovery. Constrain-based methods for causal relationship from the perspective of observational data are studied in this dissertation, the formalization and inference of causal rules are discussed, and the practical mining of direct causal relationship from massive observational databases are explored. Those systematic works may be helpful for the research of theory and practice on causal discovery from observational data.
引文
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