Efficient Proximal Gradient Algorithms for Joint Graphical Lasso

We consider learning as an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken concerning joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order methods and relatively simple, and the subproblems are solved efficiently in closed form. We further show the boundedness for the solution of the JGL problem and the iterates in the algorithms. The numerical results indicate that the proposed algorithms can achieve high accuracy and precision, and their efficiency is competitive with state-of-the-art algorithms.

Identifying Microbial Interaction Networks Based on Irregularly Spaced Longitudinal 16S rRNA sequence data

Though being vital for human health, microbial interactions with their host and with each other are still largely obscure for researchers. To deepen the understanding, the analyses based on longitudinal data are a better choice than the cross-sectional data since the information provided by the former is usually more stable. To this end, in this paper, we first propose an EM-type algorithm to identify microbial interaction network for the irregularly spaced longitudinal measurements. Correlation functions are employed to account for the correlation across the temporal measurements for a given subject. The algorithms take advantage of the efficiency of the popular graphical lasso algorithm and can be implemented straightforwardly. Simulation studies show that the proposed algorithms can significantly outperform the conventional algorithms such as graphical lasso or neighborhood method when the correlation between measurements grows larger. In second part of the paper, based on a 16S rRNA sequence data set of gut microbiome, module-preserving permutation test is proposed to test the independence of the estimated network and the phylogeny of the microbe species. The results demonstrate evidences of strong association between the interaction network and the phylogenetic tree which indicates that the taxa closer in their genomes tend to have more/stronger interactions in their functions. The proposed algorithms can be implemented through R package lglasso at \url{https://github.com/jiezhou-2/lglasso

Tailored graphical lasso for data integration in gene network reconstruction

Background Identifying gene interactions is a topic of great importance in genomics, and approaches based on network models provide a powerful tool for studying these. Assuming a Gaussian graphical model, a gene association network may be estimated from multiomic data based on the non-zero entries of the inverse covariance matrix. Inferring such biological networks is challenging because of the high dimensionality of the problem, making traditional estimators unsuitable. The graphical lasso is constructed for the estimation of sparse inverse covariance matrices in such situations, using $$L_1$$ L 1 -penalization on the matrix entries. The weighted graphical lasso is an extension in which prior biological information from other sources is integrated into the model. There are however issues with this approach, as it naïvely forces the prior information into the network estimation, even if it is misleading or does not agree with the data at hand. Further, if an associated network based on other data is used as the prior, the method often fails to utilize the information effectively. Results We propose a novel graphical lasso approach, the tailored graphical lasso, that aims to handle prior information of unknown accuracy more effectively. We provide an R package implementing the method, . Applying the method to both simulated and real multiomic data sets, we find that it outperforms the unweighted and weighted graphical lasso in terms of all performance measures we consider. In fact, the graphical lasso and weighted graphical lasso can be considered special cases of the tailored graphical lasso, and a parameter determined by the data measures the usefulness of the prior information. We also find that among a larger set of methods, the tailored graphical is the most suitable for network inference from high-dimensional data with prior information of unknown accuracy. With our method, mRNA data are demonstrated to provide highly useful prior information for protein–protein interaction networks. Conclusions The method we introduce utilizes useful prior information more effectively without involving any risk of loss of accuracy should the prior information be misleading.

Learning social networks from text data using covariate information

Accurately describing the lives of historical figures can be challenging, but unraveling their social structures perhaps is even more so. Historical social network analysis methods can help in this regard and may even illuminate individuals who have been overlooked by historians, but turn out to be influential social connection points. Text data, such as biographies, are a useful source of information for learning historical social networks but the identifcation of links based on text data can be challenging. The Local Poisson Graphical Lasso model models social networks by conditional independence structures, and leverages the number of name co-mentions in the text to infer relationships. However, this method does not take into account the abundance of covariate information that is often available in text data. Conditional independence structure like Poisson Graphical Model, which makes use name mention counts in the text can be useful tools to avoid false positive links due to the co-mentions but given historical tendency of frequently used or common names, without additional distinguishing information, we may introduce incorrect connections. In this work, we therefore extend the Local Poisson Graphical Lasso model with a (multiple) penalty structure that incorporates covariates, opening up the opportunity for similar individuals to have a higher probability of being connected. We propose both greedy and Bayesian approaches to estimate the penalty parameters. We present results on data simulated with characteristics of historical networks and show that this type of penalty structure can improve network recovery as measured by precision and recall. We also illustrate the approach on biographical data of individuals who lived in early modern Britain between 1500 and 1575. We will show how these covariates affect the statistical model’s performance using simulations, discuss how it helps to better identify links for the people with common names and those who are traditionally underrepresented in the biography text data.

An exploration of gender and prolonged grief symptoms using network analysis

Background Gender has been proposed as a potentially important predictor of bereavement outcomes. The majority of research in the field has explored this issue by examining gender differences in global grief severity. Findings have been mixed. In this study, we explore potential gender differences in grief using network analysis. This approach examines how individual symptoms relate to and reinforce each other, and so offers potential to shed light on novel aspects of grief expression across genders. Method Graphical lasso networks were constructed using self-report data from 839 spousally bereaved older participants (584 female, 255 male) collected at 2- and 11- months post-bereavement. Edge strength, node strength and global network strength were compared to identify similarities and differences between gender networks across time. Results At both time points, the strongest connection for both genders was from yearning to pangs of grief. Yearning, pangs of grief, acceptance, bitterness and shock were prominent nodes at time 1. Numbness and meaninglessness emerged as prominent nodes at time 2. Males and females differed in the relative importance of shock at time 1, and the female network had greater overall strength than the male network at time 2. Conclusions This study identified many similarities and few differences in the relationships between prolonged grief symptoms for males and females. Findings suggest that future studies should examine alternate sources of variation in grief outcomes. Limitations are discussed.

Fused Graphical Lasso Recovers Flowering Time Mutation Genes in Arabidopsis Thaliana

Conventional breeding approaches that focus on yield under highly favorable nutrient conditions have resulted in reduced genetic and trait diversity in crops. Under the growing threat from climate change, the mining of novel genes in more resilient varieties can help dramatically improve trait improvement efforts. In this work, we propose the use of the joint graphical lasso for discovering genes responsible for desired phenotypic traits. We prove its efficiency by using gene expression data for wild type and delayed flowering mutants for the model plant. Arabidopsis thaliana shows that it recovers the mutation causing genes LNK1 and LNK2. Some novel interactions of these genes were also predicted. Observing the network level changes between two phenotypes can also help develop meaningful biological hypotheses regarding the novel functions of these genes. Now that this data analysis strategy has been validated in a model plant, it can be extended to crop plants to help identify the key genes for beneficial traits for crop improvement.