Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks

Tan, Linda S. L.; Jasra, Ajay; Ebbels, Timothy M. D.

doi:10.1214/17-aoas1076

Cited by 32 publications

(31 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our experiments also indicate that larger sample sizes might be required for larger networks. While we have recommended resampling based on the importance weights when the posterior mean has deviated significantly from the initial estimate, it is also possible to consider other approaches, such as generating a new set of samples from the likelihood at the current estimate of the posterior mean or introducing some MCMC steps to restore heterogeneity (Tan et al, 2017). Here L denotes the p × p elimination matrix (Magnus and Neudecker, 1980), which has the following properties, (i) Lvec(A) = vech(A) for any square matrix A and (ii) L T vech(A) = vec(A) if A is a lower triangular matrix of order p.…”

Section: Resultsmentioning

confidence: 99%

Bayesian Variational Inference for Exponential Random Graph Models

Tan

Friel

2020

Journal of Computational and Graphical Statistics

Self Cite

View full text Add to dashboard Cite

Deriving Bayesian inference for exponential random graph models (ERGMs) is a doubly intractable problem as the normalizing constants of both the likelihood and posterior density are intractable. Markov chain Monte Carlo (MCMC) methods which yield Bayesian inference for ERGMs, such as the exchange algorithm, are asymptotically exact but computationally intensive, as a network has to be drawn from the likelihood at every step using a "tie no tie" sampler or some other algorithm. In this article, we develop a variety of variational methods for posterior density estimation and model selection, which includes nonconjugate variational message passing based on a fully adjusted pseudolikelihood and stochastic variational inference. We propose computing the unbiased gradient estimates in stochastic gradient ascent using importance sampling techniques to overcome the computational hurdle of drawing a network from the likelihood at each iteration.These methods yield approximate Bayesian inference but can be up to orders of magnitude faster than MCMC. We illustrate these variational methods using real social networks and compare their accuracy with results obtained via MCMC.

show abstract

Section: Resultsmentioning

confidence: 99%

Bayesian Variational Inference for Exponential Random Graph Models

Tan

Friel

2020

Journal of Computational and Graphical Statistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the context of multiple undirected graphs, Tan et al (2017) consider a model based on a multiplicative prior on graph structures (Chung-Lu random graph) that links the probability of edge inclusion through logistic regression. Williams et al (2019) propose a model for multiple graph aimed at the detection of network differences.…”

Section: Discussion Of Alternative Approachesmentioning

confidence: 99%

“…Usually these algorithms do not scale as well as optimization approaches based on penalized likelihood; the maximum graph size that can be analyzed depends on many factors, including type of graph, statistical model and the specific dataset on hand. In the context of multiple graphs models, alternative computational strategies have been developed and relevant instances include the EM algorithm proposed by Li et al (2020), that results in a point estimate of the graphs and can scale better to lager dimensions, and a sequential Monte Carlo (SMC) algorithm proposed by Tan et al (2017), that has similar computational performances than its MCMC counterparts.…”

Section: Discussionmentioning

confidence: 99%

Bayesian graphical models for modern biological applications

Baladandayuthapani

Vannucci

et al. 2021

Stat Methods Appl

View full text Add to dashboard Cite

Graphical models are powerful tools that are regularly used to investigate complex dependence structures in high-throughput biomedical datasets. They allow for holistic, systems-level view of the various biological processes, for intuitive and rigorous understanding and interpretations. In the context of large networks, Bayesian approaches are particularly suitable because it encourages sparsity of the graphs, incorporate prior information, and most importantly account for uncertainty in the graph structure. These features are particularly important in applications with limited sample size, including genomics and imaging studies. In this paper, we review several recently developed techniques for the analysis of large networks under non-standard settings, including but not limited to, multiple graphs for data observed from multiple related subgroups, graphical regression approaches used for the analysis of networks that change with covariates, and other complex sampling and structural settings. We also illustrate the practical utility of some of these methods using examples in cancer genomics and neuroimaging.

show abstract

“…In this way information is shared among sample groups only when appropriate. Tan et al 10 consider metabolic association networks. Their prior on graph structures is an extension of the multiplicative (or Chung‐Lu random graph) model to multiple Gaussian graphical models, linking the probability of edge inclusion through logistic regression.…”

Section: Introductionmentioning

confidence: 99%

Bayesian learning of multiple directed networks from observational data

Castelletti

Rocca

Peluso

et al. 2020

Statistics in Medicine

View full text Add to dashboard Cite

Graphical modeling represents an established methodology for identifying complex dependencies in biological networks, as exemplified in the study of co‐expression, gene regulatory, and protein interaction networks. The available observations often exhibit an intrinsic heterogeneity, which impacts on the network structure through the modification of specific pathways for distinct groups, such as disease subtypes. We propose to infer the resulting multiple graphs jointly in order to benefit from potential similarities across groups; on the other hand our modeling framework is able to accommodate group idiosyncrasies. We consider directed acyclic graphs (DAGs) as network structures, and develop a Bayesian method for structural learning of multiple DAGs. We explicitly account for Markov equivalence of DAGs, and propose a suitable prior on the collection of graph spaces that induces selective borrowing strength across groups. The resulting inference allows in particular to compute the posterior probability of edge inclusion, a useful summary for representing flow directions within the network. Finally, we detail a simulation study addressing the comparative performance of our method, and present an analysis of two protein networks together with a substantive interpretation of our findings.

show abstract

Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks

Cited by 32 publications

References 45 publications

Bayesian Variational Inference for Exponential Random Graph Models

Bayesian Variational Inference for Exponential Random Graph Models

Bayesian graphical models for modern biological applications

Bayesian learning of multiple directed networks from observational data

Contact Info

Product

Resources

About