贝叶斯网分解理论及其应用

我们生活在一个海量数据的时代。如何从高维海量数据中挖掘并研究不确定性信息，不仅是企业界、商业界关心的应用问题，也应作为我们统计领域、机器学习与数据挖掘领域所关心的核心理论问题之一。贝叶斯网作为研究不确定性问题的一个重要工具，起源于人工智能领域的研究，近年来对众多其他领域也产生了深刻影响。面对高维复杂数据，通过高维的贝叶斯网的某种分解，可以减低数据或是统计模型的复杂程度。虽然，人们在无向图模型的分解性和可压缩性研究方面取得了比较完备的结果，但是，贝叶斯网的分解理论和可压缩理论却进展缓慢。目前所有有关贝叶斯网的分解理论都是建立在贝叶斯网的道义图上。在本项目的研究中，我们要研究直接建立在贝叶斯网上的新的分解理论，并基于新的分解方式进一步研究贝叶斯网的可压缩性和结构学习。

We live in an era full of massive information and big data. How to undermine those uncertainty information from high dimensional and big data is an important question not only for industry and business areas but also for the communities of Statistics, Machine Learning and Data Mining. Bayesian network, originating from Artificial Intelligence, is a strong tool for studying those uncertainty problems. It has influenced many areas profoundly in recent years. Facing with high dimensional complex data, some decomposition of high dimensional Bayesian network can reduce the complexity of the data and statistical models. Though there are fully-fledged theories for undirected graphical models, the development of the decomposition and collapsibility is very slow for Bayesian network. Currently, all the decomposition theories for Bayesian network are basing on the moral graph of Bayesian network. In our study, we plan to build a new decomposition theory directly on Bayesian network, and develop further tools for the collapsibility and decomposition of Bayesian network.