中文摘要：

在关系分类模型的学习过程中，目前还没有类似统计学习理论中学习界限的支撑．研究关系分类的学习界限显得尤为重要，为此，提出了一些适用于关系分类模型的学习界限．首先推导出在模型假设空间有限和无限情况下的学习界限．接着提出一个衡量关系模型关联数据能力的复杂性度量——关系维，并证明了该复杂度和关系模型的生长函数之间的关系，得到有限VC维和有限关系维下的学习界限．然后分析了该界限可学习和有意义的条件，并对界限的可行性进行了详细的分析．最后分析了基于马尔可夫逻辑网的传统学习界限和关系分类中的学习情况，实验结果表明，所提出的界限能够解释实际关系分类中遇到的一些问题．

英文摘要：

Currently, there is some lack of knowledge about learning bound in relational classification model. In this study, some learning bounds for relational classification are proposed. First, two bounds are deduced for finite and infinite hypothesis space of the relational classification model respectively. Further, a complexity metric called relational dimension is proposed to measure the linking ability of the relational classification model. The relation between the complexity and growth function is proofed, and the learning bound for finite VC dimension and relational dimension is obtained. Afterwards, the condition of learnable, non-trivial, and the feasibility of the bound is analyzed. Finally, the learning progress of relational classification model based on Markov logic network is analyzed with some examples. The experimental result on a real dataset has demonstrated that the proposed bounds are useful in some practical problems.