# Efficient Inference of Spatially-varying Gaussian Markov Random Fields with Applications in Gene Regulatory Networks

arXiv: https://arxiv.org/abs/2206.10174 · HTML: https://mlsanity.com/paper/2206.10174/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 101 references that are in the map.
- First posted on arXiv 21 Jun 2022.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [DELTACON: A Principled Massive-Graph Similarity Function](https://mlsanity.com/paper/1304.4657/) (2013)
- [Graphical Lasso and Thresholding: Equivalence and Closed-form Solutions](https://mlsanity.com/paper/1708.09479/) (2017)
- [The huge Package for High-dimensional Undirected Graph Estimation in R](https://mlsanity.com/paper/2006.14781/) (2020)
- [Time-dependent spatially varying graphical models, with application to brain fMRI data analysis](https://mlsanity.com/paper/1711.03701/) (2017)
- [Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completion](https://mlsanity.com/paper/1802.04911/) (2018)
- [Joint Estimation of Precision Matrices in Heterogeneous Populations](https://mlsanity.com/paper/1601.00142/) (2016)
- [Two Sample Inference for Populations of Graphical Models with Applications to Functional Connectivity](https://mlsanity.com/paper/1502.03853/) (2015)
- [A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models](https://mlsanity.com/paper/1702.02715/) (2017)
- [Scalable Inference of Sparsely-changing Markov Random Fields with Strong Statistical Guarantees](https://mlsanity.com/paper/2102.03585/) (2021)
- [Sparse Inverse Covariance Estimation for Chordal Structures](https://mlsanity.com/paper/1711.09131/) (2017)

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

- [Solution Path of Time-varying Markov Random Fields with Discrete Regularization](https://mlsanity.com/paper/2307.13750/) (2023)

## Abstract (arXiv)

In this paper, we study the problem of inferring spatially-varying Gaussian Markov random fields (SV-GMRF) where the goal is to learn a network of sparse, context-specific GMRFs representing network relationships between genes. An important application of SV-GMRFs is in inference of gene regulatory networks from spatially-resolved transcriptomics datasets. The current work on inference of SV-GMRFs are based on the regularized maximum likelihood estimation (MLE) and suffer from overwhelmingly high computational cost due to their highly nonlinear nature. To alleviate this challenge, we propose a simple and efficient optimization problem in lieu of MLE that comes equipped with strong statistical and computational guarantees. Our proposed optimization problem is extremely efficient in practice: we can solve instances of SV-GMRFs with more than 2 million variables in less than 2 minutes. We apply the developed framework to study how gene regulatory networks in Glioblastoma are spatially rewired within tissue, and identify prominent activity of the transcription factor HES4 and ribosomal proteins as characterizing the gene expression network in the tumor peri-vascular niche that is known to harbor treatment resistant stem cells.