  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.
