# Thresholded Graphical Lasso Adjusts for Latent Variables: Application to Functional Neural Connectivity

arXiv: https://arxiv.org/abs/2104.06389 · HTML: https://mlsanity.com/paper/2104.06389/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 36 references that are in the map.
- First posted on arXiv 13 Apr 2021.

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

- [False Discoveries Occur Early on the Lasso Path](https://mlsanity.com/paper/1511.01957/) (2015)
- [On Graphical Models via Univariate Exponential Family Distributions](https://mlsanity.com/paper/1301.4183/) (2013)
- [Graphical Lasso and Thresholding: Equivalence and Closed-form Solutions](https://mlsanity.com/paper/1708.09479/) (2017)
- [On model selection consistency of regularized M-estimators](https://mlsanity.com/paper/1305.7477/) (2013)
- [Two Sample Inference for Populations of Graphical Models with Applications to Functional Connectivity](https://mlsanity.com/paper/1502.03853/) (2015)

## Built on by (most cited first, 1 of 1)

- [Fast and Accurate Graph Learning for Huge Data via Minipatch Ensembles](https://mlsanity.com/paper/2110.12067/) (2021)

## Abstract (arXiv)

In neuroscience, researchers seek to uncover the connectivity of neurons from large-scale neural recordings or imaging; often people employ graphical model selection and estimation techniques for this purpose. But, existing technologies can only record from a small subset of neurons leading to a challenging problem of graph selection in the presence of extensive latent variables. Chandrasekaran et al. (2012) proposed a convex program to address this problem that poses challenges from both a computational and statistical perspective. To solve this problem, we propose an incredibly simple solution: apply a hard thresholding operator to existing graph selection methods. Conceptually simple and computationally attractive, we demonstrate that thresholding the graphical Lasso, neighborhood selection, or CLIME estimators have superior theoretical properties in terms of graph selection consistency as well as stronger empirical results than existing approaches for the latent variable graphical model problem. We also demonstrate the applicability of our approach through a neuroscience case study on calcium-imaging data to estimate functional neural connections.