Jewel: A Novel Method for Joint Estimation of Gaussian Graphical Models

Claudia Angelini,Daniela De Canditiis,Anna Plaksienko

doi:10.3390/math9172105

Claudia Angelini, Daniela De Canditiis + Show 1 more

Open Access

https://doi.org/10.3390/math9172105

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Abstract

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix’s symmetry and the graphs’ joint learning. We solve the minimization problem using the group descend algorithm and propose two procedures for estimating the regularization parameter. Furthermore, we establish the estimator’s consistency property. Finally, we illustrate our estimator’s performance through simulated and real data examples on gene regulatory networks.

Highlights

Network analysis is becoming a powerful tool for describing the complex systems that arise in physical, biomedical, epidemiological, and social sciences, see in [1,2]
In the third experiment, we compare the performance of jewel with two existing methods, the joint graphical lasso (JGL) [14] and the proposal of Guo et al [13]
The proposed method jewel is a methodological contribution to the Gaussian Graphical Models (GGMs) inference in the context of multiple datasets

Summary

Introduction

Network analysis is becoming a powerful tool for describing the complex systems that arise in physical, biomedical, epidemiological, and social sciences, see in [1,2]. Estimating network structure and its complexity from high-dimensional data has been one of the most relevant statistical challenges of the last decade [3]. The mathematical framework to use depends on the type of relationship among the variables that the network should incorporate. In the context of gene regulatory networks (GRN), traditional co-expression methods are useful to capture marginal correlation among genes without distinguishing between direct or mediated gene interactions. Graphical models (GM) constitute a well-known framework for describing conditional dependency relationships between random variables in a complex system. They are more suited to describe direct relations among genes, not mediated by the remaining genes

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Conclusion