Learning Gaussian Graphical Models with Latent Confounders
This work addresses a common issue in network structure estimation for fields like biology and finance, but it is incremental as it builds on existing methods.
The paper tackles the problem of inferring Gaussian graphical models when data is corrupted by latent confounders, comparing LVGGM and PCA+GGM methods and proposing a new combined approach with proven consistency and convergence rates, demonstrated through simulations and real-world applications.
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.