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

TL;DR

This paper introduces an efficient optimization approach for inferring spatially-varying Gaussian Markov random fields, significantly reducing computational costs and enabling large-scale gene network analysis in spatial transcriptomics.

Contribution

The authors propose a novel, computationally efficient optimization method for SV-GMRFs with strong statistical guarantees, outperforming traditional MLE-based methods.

Findings

Able to solve large SV-GMRF instances in under 2 minutes

Identified key gene regulatory features in Glioblastoma tissue

Demonstrated practical scalability and biological relevance of the approach

Abstract

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.