高斯图模型的结构学习及应用

发布时间：2018-06-06 15:22

本文选题：图模型 + 正则化　；参考：《西北大学》2017年硕士论文

【摘要】：图模型是研究随机变量之间相依关系的重要工具,其中节点代表随机变量,边代表两个随机变量条件相依。除了节点变量外,数据常常包含协变量,协变量的存在可能影响网络结构,然而目前关于图模型的工作大多仅考虑节点变量。本文研究具有协变量的图模型结构学习问题,主要分为如下两部分:(1)在稀疏正则化的框架下,通过假设变量之间条件相依强度的参数为协变量的线性函数,建立具有协变量信息的稀疏高斯图模型,估计网络结构。所得模型具有实际解释性且易于求解。本文利用坐标下降法求解模型,实验表明含协变量比无协变量的模型效果更好,从而说明本文模型的高效性和实用性。(2)利用稀疏高斯图模型,研究我国31个省会城市及直辖市的PM2.5数据。建立这些城市PM2.5的网络结构,分析说明网络中城市节点之间的条件独立关系,并在所构建的网络的基础上,通过谱聚类方法进行社区发现。所得结果可为治霾提供参考。
[Abstract]:Graph model is an important tool to study the dependence of random variables, where nodes represent random variables and edges represent conditional dependencies of two random variables. In addition to node variables, data often contain covariables, the existence of covariables may affect the network structure, however, most of the current work on graph models only consider node variables. In this paper, the structure learning problem of graph model with covariable is studied. It is divided into two parts as follows: 1) under the framework of sparse regularization, we assume that the parameters of conditional dependence intensity among variables are linear functions of covariables. A sparse Gao Si graph model with covariable information is established to estimate the network structure. The obtained model has practical interpretation and is easy to solve. In this paper, the coordinate descent method is used to solve the model. The experiment shows that the model with covariable is more effective than the model without covariable, which shows the efficiency and practicability of the model in this paper. The PM2.5 data of 31 provincial capitals and municipalities directly under the Central Government were studied. The network structure of PM2.5 in these cities is established, and the conditional independent relationship between urban nodes in the network is analyzed. On the basis of the constructed network, community discovery is carried out by spectral clustering method. The results can provide a reference for the treatment of haze.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5;X513

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