Tailored graphical lasso for data integration in gene network reconstruction

A framework for analyzing EEG data using high-dimensional tests

MOTIVATION

The objective of EEG data analysis is to extract meaningful insights, enhancing our understanding of brain function. However, the high dimensionality and temporal dependency of EEG data present significant challenges to the effective application of statistical methods. This study systematically addresses these challenges by introducing a high-dimensional statistical framework that includes testing changes in the mean vector and precision matrix, as well as conducting relevant analyses. Specifically, the Ridgelized Hotelling's T2 test (RIHT) is introduced to test changes in the mean vector of EEG data over time while relaxing traditional distributional and moment assumptions. Secondly, a multiple population de-biased estimation and testing method (MPDe) is developed to estimate and simultaneously test differences in the precision matrix before and after stimulation. This approach extends the joint Gaussian graphical model to multiple populations while incorporating the temporal dependency of EEG data. Meanwhile, a novel data-driven fine-tuning method is applied to automatically search for optimal hyperparameters.

RESULTS

Through comprehensive simulation studies and applications, we have obtained substantial evidence to validate that the RIHT has relatively high power, and it can test for changes when the distribution is unknown. Similarly, the MPDe can infer the precision matrix under time-dependent conditions. Additionally, the conducted analysis of channel selection and dominant channel can identify significant channels which play a crucial role in human cognitive ability, such as PO3, PO4, Pz, P4, P8, FT7, and FT8. All findings confirm that the proposed methods outperform existing ones, demonstrating the effectiveness of the framework in EEG data analysis.

AVAILABILITY AND IMPLEMENTATION

Source code and data used in the article are available at https://github.com/yahu911/Framework_EEG.

Reassessing the modularity of gene co-expression networks using the Stochastic Block Model

Finding communities in gene co-expression networks is a common first step toward extracting biological insight from these complex datasets. Most community detection algorithms expect genes to be organized into assortative modules, that is, groups of genes that are more associated with each other than with genes in other groups. While it is reasonable to expect that these modules exist, using methods that assume they exist a priori is risky, as it guarantees that alternative organizations of gene interactions will be ignored. Here, we ask: can we find meaningful communities without imposing a modular organization on gene co-expression networks, and how modular are these communities? For this, we use a recently developed community detection method, the weighted degree corrected stochastic block model (SBM), that does not assume that assortative modules exist. Instead, the SBM attempts to efficiently use all information contained in the co-expression network to separate the genes into hierarchically organized blocks of genes. Using RNAseq gene expression data measured in two tissues derived from an outbred population of Drosophila melanogaster, we show that (a) the SBM is able to find ten times as many groups as competing methods, that (b) several of those gene groups are not modular, and that (c) the functional enrichment for non-modular groups is as strong as for modular communities. These results show that the transcriptome is structured in more complex ways than traditionally thought and that we should revisit the long-standing assumption that modularity is the main driver of the structuring of gene co-expression networks.

Reassessing the modularity of gene co-expression networks using the Stochastic Block Model

Finding communities in gene co-expression networks is a common first step toward extracting biological insight from these complex datasets. Most community detection algorithms expect genes to be organized into assortative modules, that is, groups of genes that are more associated with each other than with genes in other groups. While it is reasonable to expect that these modules exist, using methods that assume they exist a priori is risky, as it guarantees that alternative organizations of gene interactions will be ignored. Here, we ask: can we find meaningful communities without imposing a modular organization on gene co-expression networks, and how modular are these communities? For this, we use a recently developed community detection method, the weighted degree corrected stochastic block model (SBM), that does not assume that assortative modules exist. Instead, the SBM attempts to efficiently use all information contained in the co-expression network to separate the genes into hierarchically organized blocks of genes. Using RNA-seq gene expression data measured in two tissues derived from an outbred population of Drosophila melanogaster, we show that (a) the SBM is able to find ten times as many groups as competing methods, that (b) several of those gene groups are not modular, and that (c) the functional enrichment for non-modular groups is as strong as for modular communities. These results show that the transcriptome is structured in more complex ways than traditionally thought and that we should revisit the long-standing assumption that modularity is the main driver of the structuring of gene co-expression networks.

StabJGL: a stability approach to sparsity and similarity selection in multiple-network reconstruction

Motivation

In recent years, network models have gained prominence for their ability to capture complex associations. In statistical omics, networks can be used to model and study the functional relationships between genes, proteins, and other types of omics data. If a Gaussian graphical model is assumed, a gene association network can be determined from the non-zero entries of the inverse covariance matrix of the data. Due to the high-dimensional nature of such problems, integrative methods that leverage similarities between multiple graphical structures have become increasingly popular. The joint graphical lasso is a powerful tool for this purpose, however, the current AIC-based selection criterion used to tune the network sparsities and similarities leads to poor performance in high-dimensional settings.

Results

We propose stabJGL, which equips the joint graphical lasso with a stable and well-performing penalty parameter selection approach that combines the notion of model stability with likelihood-based similarity selection. The resulting method makes the powerful joint graphical lasso available for use in omics settings, and outperforms the standard joint graphical lasso, as well as state-of-the-art joint methods, in terms of all performance measures we consider. Applying stabJGL to proteomic data from a pan-cancer study, we demonstrate the potential for novel discoveries the method brings.

Availability and implementation

A user-friendly R package for stabJGL with tutorials is available on Github https://github.com/Camiling/stabJGL.