Gaussian Graphical models (GGM) are widely used to estimate the network structures in many applications ranging from biology to finance. In practice, data is often corrupted by latent confounders which biases inference of the underlying true graphical structure. In this paper, we compare and contrast two strategies for inference in graphical models with latent confounders: Gaussian graphical models with latent variables (LVGGM) and PCA-based removal of confounding (PCA+GGM). While these two approaches have similar goals, they are motivated by different assumptions about confounding. In this paper, we explore the connection between these two approaches and propose a new method, which combines the strengths of these two approaches. We prove the consistency and convergence rate for the PCA-based method and use these results to provide guidance about when to use each method. We demonstrate the effectiveness of our methodology using both simulations and in two real-world applications.
翻译:Gausian图形模型(GGM)被广泛用来估计网络结构,从生物学到金融等许多应用中的网络结构。在实践中,数据常常被潜在混淆者腐蚀,从而偏向于真实图形结构背后的推论。在本文中,我们比较和对比了图形模型中与潜在混淆者推论的两个战略:高西亚图形模型与潜在变量(LVGGM)和五氯苯甲醚脱钩(PCA+GGM) 。这两种方法有着相似的目标,但它们的动机是对于混淆的不同假设。在本文中,我们探讨了这两种方法之间的联系,并提出了一种新方法,将这两种方法的长处结合起来。我们证明了以五氯苯为基础的方法的一致性和趋同率,并用这些结果指导何时使用每种方法。我们用模拟和两种真实世界应用来证明我们方法的有效性。