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242
An Empirical Bayes Approach to Inferring LargeScale Gene Association Networks
 BIOINFORMATICS
, 2004
"... Motivation: Genetic networks are often described statistically by graphical models (e.g. Bayesian networks). However, inferring the network structure offers a serious challenge in microarray analysis where the sample size is small compared to the number of considered genes. This renders many standar ..."
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Cited by 151 (6 self)
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Motivation: Genetic networks are often described statistically by graphical models (e.g. Bayesian networks). However, inferring the network structure offers a serious challenge in microarray analysis where the sample size is small compared to the number of considered genes. This renders many standard algorithms for graphical models inapplicable, and inferring genetic networks an “illposed” inverse problem. Methods: We introduce a novel framework for smallsample inference of graphical models from gene expression data. Specifically, we focus on socalled graphical Gaussian models (GGMs) that are now frequently used to describe gene association networks and to detect conditionally dependent genes. Our new approach is based on (i) improved (regularized) smallsample point estimates of partial correlation, (ii) an exact test of edge inclusion with adaptive estimation of the degree of freedom, and (iii) a heuristic network search based on false discovery rate multiple testing. Steps (ii) and (iii) correspond to an empirical Bayes estimate of the network topology. Results: Using computer simulations we investigate the sensitivity (power) and specificity (true negative rate) of the proposed framework to estimate GGMs from microarray data. This shows that it is possible to recover the true network topology with high accuracy even for smallsample data sets. Subsequently, we analyze gene expression data from a breast cancer tumor study and illustrate our approach by inferring a corresponding largescale gene association network for 3,883 genes. Availability: The authors have implemented the approach in the R package “GeneTS ” that is freely available from
ARACNE: An algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context
 BMC Bioinformatics , Suppl
, 2006
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Tractable learning of large bayes net structures from sparse data
, 2004
"... statistics for creating the global Bayes Net. This paper addresses three questions. Is it useful to attempt to learn a Bayesian network structure with hundreds of thousands of nodes? How should such structure search proceed practically? The third question arises out of our approach to the second: ho ..."
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Cited by 31 (4 self)
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statistics for creating the global Bayes Net. This paper addresses three questions. Is it useful to attempt to learn a Bayesian network structure with hundreds of thousands of nodes? How should such structure search proceed practically? The third question arises out of our approach to the second: how can Frequent Sets (Agrawal et al., 1993), which are extremely popular in the area of descriptive data mining, be turned into a probabilistic model? Large sparse datasets with hundreds of thousands of records and attributes appear in social networks, warehousing, supermarket transactions and web logs. The complexity of structural search made learning of factored probabilistic models on such datasets unfeasible. We propose to use Frequent Sets to significantly speed up the structural search. Unlike previous approaches, we not only cache nway sufficient statistics, but also exploit their local structure. We also present an empirical evaluation of our algorithm applied to several massive datasets.
A robust procedure for gaussian graphical model search from microarray data with p larger than n
 Journal of Machine Learning Research
, 2006
"... Learning of largescale networks of interactions from microarray data is an important and challenging problem in bioinformatics. A widely used approach is to assume that the available data constitute a random sample from a multivariate distribution belonging to a Gaussian graphical model. As a conse ..."
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Cited by 28 (4 self)
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Learning of largescale networks of interactions from microarray data is an important and challenging problem in bioinformatics. A widely used approach is to assume that the available data constitute a random sample from a multivariate distribution belonging to a Gaussian graphical model. As a consequence, the prime objects of inference are fullorder partial correlations which are partial correlations between two variables given the remaining ones. In the context of microarray data the number of variables exceed the sample size and this precludes the application of traditional structure learning procedures because a sampling version of fullorder partial correlations does not exist. In this paper we consider limitedorder partial correlations, these are partial correlations computed on marginal distributions of manageable size, and provide a set of rules that allow one to assess the usefulness of these quantities to derive the independence structure of the underlying Gaussian graphical model. Furthermore, we introduce a novel structure learning procedure based on a quantity, obtained from limitedorder partial correlations, that we call the nonrejection rate. The applicability and usefulness of the procedure are demonstrated by both simulated and real data.
Generating realistic in silico gene networks for performance assessment of reverse engineering methods
 J. Comput. Biol
"... This eprint is identical in content to the postprint of this article, which is available at www.liebertonline.com/cmb. Related articles are available ..."
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Cited by 22 (2 self)
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This eprint is identical in content to the postprint of this article, which is available at www.liebertonline.com/cmb. Related articles are available
Entropy Inference and the JamesStein Estimator, with Application to Nonlinear Gene Association Networks
"... We present a procedure for effective estimation of entropy and mutual information from smallsample data, and apply it to the problem of inferring highdimensional gene association networks. Specifically, we develop a JamesSteintype shrinkage estimator, resulting in a procedure that is highly effic ..."
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Cited by 16 (1 self)
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We present a procedure for effective estimation of entropy and mutual information from smallsample data, and apply it to the problem of inferring highdimensional gene association networks. Specifically, we develop a JamesSteintype shrinkage estimator, resulting in a procedure that is highly efficient statistically as well as computationally. Despite its simplicity, we show that it outperforms eight other entropy estimation procedures across a diverse range of sampling scenarios and datagenerating models, even in cases of severe undersampling. We illustrate the approach by analyzing E. coli gene expression data and computing an entropybased geneassociation network from gene expression data. A computer program is available that implements the proposed shrinkage estimator. Keywords: entropy, shrinkage estimation, JamesStein estimator, “small n, large p ” setting, mutual information, gene association network
Modelling gene networks at different organisational levels
 FEBS LETT
, 2005
"... Approaches to modelling gene regulation networks can be categorized, according to increasing detail, as network parts lists, network topology models, network control logic models, or dynamic models. We discuss the current state of the art for each of these approaches. There is a gap between the par ..."
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Cited by 14 (1 self)
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Approaches to modelling gene regulation networks can be categorized, according to increasing detail, as network parts lists, network topology models, network control logic models, or dynamic models. We discuss the current state of the art for each of these approaches. There is a gap between the parts list and topology models on one hand, and control logic and dynamic models on the other hand. The first two classes of models have reached a genomewide scale, while for the other model classes high throughput technologies are yet to make a major impact.
Identifying functional modules in proteinprotein interaction networks: an integrated exact approach
 Bioinformatics
, 2008
"... Motivation: With the exponential growth of expression and proteinprotein interaction (PPI) data, the frontier of research in system biology shifts more and more to the integrated analysis of these large datasets. Of particular interest is the identification of functional modules in PPI networks, sha ..."
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Cited by 13 (1 self)
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Motivation: With the exponential growth of expression and proteinprotein interaction (PPI) data, the frontier of research in system biology shifts more and more to the integrated analysis of these large datasets. Of particular interest is the identification of functional modules in PPI networks, sharing common cellular function beyond the scope of classical pathways, by means of detecting differentially expressed regions in PPI networks. This requires on the one hand an adequate scoring of the nodes in the network to be identified and on the other hand the availability of an effective algorithm to find the maximally scoring network regions. Various heuristic approaches have been proposed in the literature. Results: Here we present the first exact solution for this problem, which is based on integer linear programming and its connection to the wellknown prizecollecting Steiner tree problem from Operations