含有隐变量的因果结构学习与统计因果推断

The exploration for causal relationships between complex objects is one of the important contents in philosophy, natural sciences, social sciences and so on. The introduction of latent variables can illustrate the causal relationships between complex objects better, and it is convenient for effective statistical analysis. Since latent variables can not be observed, they bring us not only a lot of convenience but also many difficulties. Causal structure learning and causal inference with latent variables is a hot and difficult topic in many research fields. This project learns the causal structures with latent variables from two different facets. One method uses the ideas of decomposition and local learning. It decomposes the structure learning of a causal network with latent variables into some subproblems, and integrates the local learning structures to obtain global causal structures. This method reduces the difficulty of the problem and improves the efficiency of the algorithm. The other method studies the structure learning of semi-markovian causal models. Based on the existing learning methods, we study the optimal design of interventional experiments in order to orient the unknown directions of edges, and detect the undiscovered bi-directed edges from further tests. Finally we get a correct and effective learning method. In this project, when the causal structures are unknown, we study the estimations of interventional effects from observational data, propose a new definition of confounder, and give some conditions for judging confounders and a method for detecting confounders. Hopefully, our results will not only promote the further development of theories in causal researches, but also provide some advice for practical use.

探索复杂事物之间的因果关系是哲学、自然科学和社会科学等几乎所有科学研究的一个重要内容。为了便于解释复杂事物间的因果关系并进行有效的统计分析，研究者们引入隐变量。由于隐变量不能被观测，它给人们带来便利的同时也带来很多困难。含有隐变量的因果结构学习与因果推断是许多领域中的一个研究热点和难点。本项目从两个不同角度给出含有隐变量的因果结构学习方法。方法一采用分解和局部学习的思想，将含隐变量因果网的结构学习问题分解为一些子问题，并整合局部学习结构得到全局因果结构，降低问题的难度同时提高算法的效率。方法二针对半马尔可夫因果模型结构学习的问题，给出边定向的干预试验的最优设计方法，并进一步探测未发现的双向边，得到一个正确而有效的学习方法。在因果结构未知时，本项目研究由观测数据估计干预效应的方法，提出混杂子的新定义，给出其判定条件和探测方法。我们的成果将推动因果研究理论的进一步发展，并为指导实践提供依据。

该项目研究了含有隐变量的因果结构学习和因果结构未知时的统计因果推断方法。对于结构学习问题，我们分别研究了高斯图模型和层次模型的结构学习方法，给出将全局问题分解为局部问题的计算方法，研究了所提出方法的性质，发现我们的方法降低了问题的复杂度，提高了计算的速度，在生物基因等数据的分析中具有良好的表现。对于朴素贝叶斯分类器的特征筛选问题，我们给出一种L0正则化的估计方法，并研究了估计的渐近统计性质，验证了我们方法在实际数据中具有良好的表现。对于因果结构未知时的统计因果推断方法，我们研究了带有追踪的随机化实验中数据被死亡截断的情形，我们应用Balke-Pearl线性规划算法得到幸存平均因果效应(SACE)的一种简单的边界表达式；对于带有不依从的随机化实验，基于对VanderWeele(2008)和Chiba(2009)方法的研究，我们提出应用可观测的协变量信息来给出平均因果效应的一个新的可达边界，并比较了三种边界在不同条件下的表现，为实际领域的工作者进行有效的平均因果效应分析提供了参考。