arXiv subjects

E. C. Wit

Publications and source records attributed to E. C. Wit.

3 recordsLinked to original sources

arXiv2019

Bayesian Structure Learning in Sparse Gaussian Graphical Models

Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence of variables through the presence or absence of edges in the underlying graph. In this paper, we introduce a novel and efficient Bayesian framework for Gaussian graphical model determination which is a trans-dimensional Markov Chain Monte Carlo (MCMC) approach based on a continuous-time birth-death process. We cover the theory and computational details of the method. It is easy to implement and computationally feasible for high-dimensional graphs. We show our method outperforms alternative Bayesian approaches in terms of convergence, mixing in the graph space and computing time. Unlike frequentist approaches, it gives a principled and, in practice, sensible approach for structure learning. We illustrate the efficiency of the method on a broad range of simulated data. We then apply the method on large-scale real applications from human and mammary gland gene expression studies to show its empirical usefulness. In addition, we implemented the method in the R package BDgraph which is freely available at http://CRAN.R-project.org/package=BDgraph

stat.ME↗

arXiv2017

Detecting Epistatic Selection with Partially Observed Genotype Data Using Copula Graphical Models

Recombinant Inbred Lines derived from divergent parental lines can display extensive segregation distortion and long-range linkage disequilibrium (LD) between distant loci. These genomic signatures are consistent with epistatic selection during inbreeding. Epistatic interactions affect growth and fertility traits or even cause complete lethality. Detecting epistasis is challenging as multiple testing approaches are under-powered and true long-range LD is difficult to distinguish from drift. Here we develop a method for reconstructing an underlying network of genomic signatures of high-dimensional epistatic selection from multi-locus genotype data. The network captures the conditionally dependent short- and long-range LD structure and thus reveals "aberrant" marker-marker associations that are due to epistatic selection rather than gametic linkage. The network estimation relies on penalized Gaussian copula graphical models, which accounts for a large number of markers p and a small number of individuals n. A multi-core implementation of our algorithm makes it feasible to estimate the graph in high-dimensions also in the presence of significant portions of missing data. We demonstrate the efficiency of the proposed method on simulated datasets as well as on genotyping data in A.thaliana and maize. In addition, we implemented the method in the R package netgwas which is freely available at https://CRAN.R-project.org/package=netgwas.

stat.AP↗

arXiv2012

Factorial graphical lasso for dynamic networks

Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this paper we focus on determining network structure. Estimating dynamic networks is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is bigger than the number of observations. However, a characteristic of many networks is that they are sparse. For example, the molecular structure of genes make interactions with other components a highly-structured and therefore sparse process. Penalized Gaussian graphical models have been used to estimate sparse networks. However, the literature has focussed on static networks, which lack specific temporal constraints. We propose a structured Gaussian dynamical graphical model, where structures can consist of specific time dynamics, known presence or absence of links and block equality constraints on the parameters. Thus, the number of parameters to be estimated is reduced and accuracy of the estimates, including the identification of the network, can be tuned up. Here, we show that the constrained optimization problem can be solved by taking advantage of an efficient solver, logdetPPA, developed in convex optimization. Moreover, model selection methods for checking the sensitivity of the inferred networks are described. Finally, synthetic and real data illustrate the proposed methodologies.

stat.ME↗