A network model that combines latent factors and sparse graphs
A network model that combines latent factors and sparse graphs
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DOI：
10.1002/sam.11492
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发表时间：
2020-12
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通讯作者：
Namjoon Suh;X. Huo;Eric Heim;Lee M. Seversky
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作者：
Namjoon Suh;X. Huo;Eric Heim;Lee M. Seversky
提出了一种将潜在因素模型和稀疏图形模型相结合的网络数据模型。值得注意的是，无论是潜在因素模型还是稀疏图形模型本身都不足以捕捉数据的结构。建议的模型有一个潜在的(即，因素分析)模型来表示主要趋势(也称为因素)，以及一个稀疏的图形组件来捕捉剩余的特殊依赖关系。模型选择和参数估计通过惩罚似然方法同时进行。目标函数的凸性使得我们可以开发一种高效的算法，而惩罚项则倾向于低维潜在成分和稀疏的图形结构。通过模拟研究验证了该模型的有效性，并将该模型应用于四个真实的数据集：扎卡里的空手道俱乐部数据、克雷布的美国政治书籍数据集(http://www.orgnet.com)，美国政治博客数据集)和统计学家引文网络，在实际情况中显示了有意义的表现。
We propose a combined model, which integrates the latent factor model and a sparse graphical model, for network data. It is noticed that neither a latent factor model nor a sparse graphical model alone may be sufficient to capture the structure of the data. The proposed model has a latent (i.e., factor analysis) model to represent the main trends (a.k.a., factors), and a sparse graphical component that captures the remaining ad‐hoc dependence. Model selection and parameter estimation are carried out simultaneously via a penalized likelihood approach. The convexity of the objective function allows us to develop an efficient algorithm, while the penalty terms push towards low‐dimensional latent components and a sparse graphical structure. The effectiveness of our model is demonstrated via simulation studies, and the model is also applied to four real datasets: Zachary's Karate club data, Kreb's U.S. political book dataset ( http://www.orgnet.com), U.S. political blog dataset , and citation network of statisticians; showing meaningful performances in practical situations.