关于高斯图模型在配对数据问题中的应用
On the application of Gaussian graphical models to paired data problems
AI总结：
研究高斯图模型在配对数据中的应用，提出融合图形套索惩罚学习两个相依图及跨图关联结构，并提供ADMM算法与R包，应用于癌症基因组学比较。
摘要：
高斯图模型如今被普遍应用于比较共享相同变量的多个组，通过联合学习它们的独立性结构。我们考虑恰好存在两个相依组的情况，其关联结构由一族适用于处理配对数据问题的彩色高斯图模型表示。为了学习这两个相依图及其跨图关联结构，我们实现了一个融合图形套索惩罚。我们对这种方法进行了全面分析，特别关注一些相关子模型类所扮演的角色。通过这种方式，我们为高斯图模型在配对数据问题中的应用提供了一套广泛的工具。这些工具包括用于指定惩罚值以获得套索解路径的结果，以及一个求解融合图形套索优化问题的 ADMM 算法。最后，我们展示了该方法在癌症基因组学中的应用，其中比较癌细胞与来自肿瘤邻近组织学正常组织的对照样本具有重要意义。本文描述的所有方法均在 $\ exttt{R}$ 包 $\ exttt{pdglasso}$ 中实现，可在 https://github.com/savranciati/pdglasso 获取。
英文摘要：
Gaussian graphical models are nowadays commonly applied to the comparison of groups sharing the same variables, by jointy learning their independence structures. We consider the case where there are exactly two dependent groups and the association structure is represented by a family of coloured Gaussian graphical models suited to deal with paired data problems. To learn the two dependent graphs, together with their across-graph association structure, we implement a fused graphical lasso penalty. We carry out a comprehensive analysis of this approach, with special attention to the role played by some relevant submodel classes. In this way, we provide a broad set of tools for the application of Gaussian graphical models to paired data problems. These include results useful for the specification of penalty values in order to obtain a path of lasso solutions and an ADMM algorithm that solves the fused graphical lasso optimization problem. Finally, we present an application of our method to cancer genomics where it is of interest to compare cancer cells with a control sample from histologically normal tissues adjacent to the tumor. All the methods described in this article are implemented in the $\texttt{R}$ package $\texttt{pdglasso}$ availabe at: https://github.com/savranciati/pdglasso.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
