# Learning Gaussian Graphical Models with Latent Confounders

arXiv: https://arxiv.org/abs/2105.06600 · HTML: https://mlsanity.com/paper/2105.06600/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 55 references that are in the map.
- First posted on arXiv 14 May 2021.

## Builds on (most cited first, 5 of 5)

- [A convex pseudo-likelihood framework for high dimensional partial correlation estimation with convergence guarantees](https://mlsanity.com/paper/1307.5381/) (2013)
- [The huge Package for High-dimensional Undirected Graph Estimation in R](https://mlsanity.com/paper/2006.14781/) (2020)
- [Learning Latent Variable Gaussian Graphical Models](https://mlsanity.com/paper/1406.2721/) (2014)
- [Joint Nonparametric Precision Matrix Estimation with Confounding](https://mlsanity.com/paper/1810.07147/) (2018)
- [Ising Models with Latent Conditional Gaussian Variables](https://mlsanity.com/paper/1901.09712/) (2019)

## Abstract (arXiv)

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.