关联结构学习在数据分析中至关重要，非高斯性和关联复杂性是其应用中两个主要的难题。Copula理论提供了在分离边缘函数的同时表达各种关联关系的工具，为难题的解决开辟了路径。本文基于Copula函数对统计关联结构的表达，研究了三个问题：Copula函数与互信息（Mutual Information：MI）的关系问题。Copula函数和MI构成了关联关系的表示和度量的两个方面。证明了MI是负的Copula函数的熵，称为Copula熵，指出了MI是Copula函数包含的随机性的度量。据此提出了基于经验Copula函数的熵估计的互信息估计方法。基于Copula的显结构学习问题。从Copula函数角度解释了概率图结构的基本概念；说明了图模型是Copula函数的一种特例--Copula积。提出了基于Copula的结构学习框架，定义了Copula似然的概念作为框架的全局指标。Copula似然与变量自身特性无关，比基于全局概率的似然更符合结构学习问题。设计了新框架下树形结构和嵌套结构的学习方法。实验表明了Copula结构学习较传统结构学习的优越性。基于Copula的隐结构学习问题，称为Copula元分析（Copula Component Analysis：CCA）。CCA是基于观测数据估计满足Copula关联结构的源变量。通过引入Copula函数结构，使元分析问题的隐含变量突破了已有方法独立性假设的限制，扩展到任意关联关系的情况。通过研究在K-L散度意义下CCA问题，指出了求解空间中目标和假设空间间距离的几何性质，进而提出了基于似然准则的梯度求解方法。仿真实验表明CCA在相关的元素分析问题上优于独立元分析。

Dependence structure learning is of significant importance in data analysis. Non-Gaussianity and Dependency Complexity are two main problems in its applications. Copula theory provides a mathematical tool that can represent all types of dependence relations between random variables while separated with margins, as a solution to the above problems. This thesis studies three topics based on copula representation:Copula function and Mutual Information (MI). MI is proved to be actually negative entropy of copula, named copula entropy, hence MI can be interpreted as the measure of uncertainty represented by copula. A method for MI estimation based on estimating entropy of empirical copula is proposed.Structure learning based on copula. The basic concepts of probabilistic graphical models (GM) are interpreted by means of copula and then GM is shown as a special case of copula function, i.e. product copula. A structure learning framework based on copula is proposed and copula likelihood is defined as the criteria of learning. Since irrelevance of the properties of individual variables, copula likelihood is better than traditional likelihood as a criteria for the problem. the learning methods for tree and nested structure are designed. Experiments show copula structure learning has the advantages over the traditional methods.Copula component analysis (CCA). CCA is defined to recover from observations the sources specified by copula. By incorporating copula, the models with the assumption of independent sources, like independent component analysis (ICA), are generalized to the case with dependent sources. In a sense of K-L divergence, the geometrical property of CCA is studied and then a gradient-based solution to CCA under the guidance of ML criteria is suggested. Simulation experiments show CCA can outperform ICA when sources are dependent.