含潜在混杂因子的高斯图模型学习
Learning Gaussian Graphical Models with Latent Confounders
AI总结：
针对潜在混杂因子干扰高斯图模型结构推断的问题，本文探究了LVGGM与PCA+GGM两种推断策略的关联，提出融合二者优势的新方法，证明了PCA类方法的一致性与收敛速率，给出方法选用指导，并通过模拟和真实应用验证了有效性。
摘要：
高斯图模型（Gaussian Graphical models, GGM）被广泛用于估计从生物学到金融等诸多应用中的网络结构。在实际应用中，数据常被潜在混杂因子干扰，这会使对底层真实图结构的推断产生偏差。本文对比了存在潜在混杂因子时图模型推断的两种策略：含潜在变量的高斯图模型（Gaussian graphical models with latent variables, LVGGM）和基于PCA的混杂因子去除方法（PCA+GGM）。尽管这两种方法目标相近，但其背后的混杂假设各不相同。本文探究了两种方法之间的关联，并提出了一种融合二者优势的新方法。我们证明了基于PCA的方法的一致性和收敛速率，并利用这些结果为不同场景下应选用哪种方法提供指导。我们通过模拟实验和两个真实世界应用验证了所提方法的有效性。
英文摘要：
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.
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