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173
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 236 (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
Exact Bayesian structure discovery in Bayesian networks
 J. of Machine Learning Research
, 2004
"... We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n2 n) time, where n is the number of attributes; the number of parents per ..."
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Cited by 115 (12 self)
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We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n2 n) time, where n is the number of attributes; the number of parents per attribute is bounded by a constant. In this paper we show that the posterior probabilities for all the n(n−1) potential edges can be computed in O(n2 n) total time. This result is achieved by a forward–backward technique and fast Möbius transform algorithms, which are of independent interest. The resulting speedup by a factor of about n 2 allows us to experimentally study the statistical power of learning moderatesize networks. We report results from a simulation study that covers data sets with 20 to 10,000 records over 5 to 25 discrete attributes. 1
An effective structure learning method for constructing gene networks
 Bioinformatics
, 2006
"... Motivation: Bayesian network methods have shown promise in gene regulatory network reconstruction because of their capability of capturing causal relationships between genes and handling data with noises found in biological experiments. The problem of learning network structures, however, is NP hard ..."
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Cited by 31 (1 self)
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Motivation: Bayesian network methods have shown promise in gene regulatory network reconstruction because of their capability of capturing causal relationships between genes and handling data with noises found in biological experiments. The problem of learning network structures, however, is NP hard. Consequently, heuristic methods such as hill climbing are used for structure learning. For networks of a moderate size, hill climbing methods are not computationally efficient. Furthermore, relatively low accuracy of the learned structures may be observed. The purpose of this paper is to present a novel structure learning method for gene network discovery.. Results: In this paper, we present a novel structure learning method to reconstruct the underlying gene networks from the observational gene expression data. Unlike hill climbing approaches, the proposed method first constructs an undirected network based on mutual information between two nodes and then split the structure into substructures. The directional orientations for the edges that connect two nodes are then obtained by optimizing a scoring function for each substructure. Our method is evaluated using two benchmark network datasets with known structures. The results show that the proposed method can identify networks that are close to the optimal structures. It outperforms hill climbing methods in terms of both computation time and predicted structure accuracy. We also apply the method to gene expression data measured during the yeast cycle and show the effectiveness of the proposed method for network reconstruction.
Bayesian structure learning using dynamic programming and MCMC
 In UAI, 2007b
"... We show how to significantly speed up MCMC sampling of DAG structures by using a powerful nonlocal proposal based on Koivisto’s dynamic programming (DP) algorithm (11; 10), which computes the exact marginal posterior edge probabilities by analytically summing over orders. Furthermore, we show how s ..."
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Cited by 30 (1 self)
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We show how to significantly speed up MCMC sampling of DAG structures by using a powerful nonlocal proposal based on Koivisto’s dynamic programming (DP) algorithm (11; 10), which computes the exact marginal posterior edge probabilities by analytically summing over orders. Furthermore, we show how sampling in DAG space can avoid subtle biases that are introduced by approaches that work only with orders, such as Koivisto’s DP algorithm and MCMC order samplers (6; 5). 1
Cryptanalysis of the Cellular Message Encryption Algorithm By David Wagner Bruce Schneier John Kelsey i
 IEEE/ACM Trans. Comput. Biol. Bioinform
, 2005
"... Abstract—We construct a genetogene regulatory network from timeseries data of expression levels for the whole genome of the yeast Saccharomyces cerevisae, in a case where the number of measurements is much smaller than the number of genes in the network. This network is analyzed with respect to p ..."
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Cited by 27 (1 self)
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Abstract—We construct a genetogene regulatory network from timeseries data of expression levels for the whole genome of the yeast Saccharomyces cerevisae, in a case where the number of measurements is much smaller than the number of genes in the network. This network is analyzed with respect to present biological knowledge of all genes (according to the Gene Ontology database), and we find some of its largescale properties to be in accordance with known facts about the organism. The linear modeling employed here has been explored several times, but due to lack of any validation beyond investigating individual genes, it has been seriously questioned with respect to its applicability to biological systems. Our results show the adequacy of the approach and make further investigations of the model meaningful. Index Terms—Biology and genetics, time series analysis, network problems, gene network, network inference, Lasso, yeast, validation, outdegree. æ 1
Applying dynamic bayesian networks to perturbed gene expression data
 BMC bioinformatics
, 2006
"... Abstract Motivation: A central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayes ..."
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Cited by 24 (2 self)
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Abstract Motivation: A central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayesian networks appear attractive in the field of inferring gene interactions structure from microarray experiments data. However, the basic formalism has some disadvantages, e.g. it is sometimes hard to distinguish between the origin and the object of an interaction. Two kinds of microarray experiments yield data particularly rich in information regarding the direction of interactions: time series and perturbation experiments. In order to correctly handle them, the basic formalism must be modified. For example, dynamic Bayesian networks apply to time series microarray data. Results: We extend the framework of dynamic Bayesian networks in order to handle perturbations. A new discretization method, specialized for datasets from time series perturbations experiments, is also introduced. We compare networks inferred from realistic simulations data by our method and by dynamic Bayesian networks learning techniques. We conclude that application of our method substantially improves inferring. 1 Introduction As most genetic regulatory systems involve many components connected through complex networks of interactions, formal methods and computer tools for modeling and simulating are needed. Therefore, various formalisms were proposed to describe genetic regulatory systems, including Boolean networks and their generalizations, ordinary and partial differential equations, stochastic equations and Bayesian networks (see [4] for a review). While differential and stochastic equations describe the biophysical processes at a very refined level of detail and prove useful in simulations of well studied systems, Bayesian networks appear attractive in the field of inferring the regulatory network structure from gene expression data. The reason is that their learning techniques have solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way.
2006) Computational inference of neural information flow networks PLoS Computational Biology 2:e161
, 2006
"... Determining how information flows along anatomical brain pathways is a fundamental requirement for understanding how animals perceive their environments, learn, and behave. Attempts to reveal such neural information flow have been made using linear computational methods, but neural interactions are ..."
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Cited by 23 (6 self)
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Determining how information flows along anatomical brain pathways is a fundamental requirement for understanding how animals perceive their environments, learn, and behave. Attempts to reveal such neural information flow have been made using linear computational methods, but neural interactions are known to be nonlinear. Here, we demonstrate that a dynamic Bayesian network (DBN) inference algorithm we originally developed to infer nonlinear transcriptional regulatory networks from gene expression data collected with microarrays is also successful at inferring nonlinear neural information flow networks from electrophysiology data collected with microelectrode arrays. The inferred networks we recover from the songbird auditory pathway are correctly restricted to a subset of known anatomical paths, are consistent with timing of the system, and reveal both the importance of reciprocal feedback in auditory processing and greater information flow to higherorder auditory areas when birds hear natural as opposed to synthetic sounds. A linear method applied to the same data incorrectly produces networks with information flow to nonneural tissue and over paths known not to exist. To our knowledge, this study represents the first biologically validated demonstration of an algorithm to successfully infer neural information flow networks.
Xiao G: Comparing statistical methods for constructing large scale gene networks. PLoS One 2012
"... The gene regulatory network (GRN) reveals the regulatory relationships among genes and can provide a systematic understanding of molecular mechanisms underlying biological processes. The importance of computer simulations in understanding cellular processes is now widely accepted; a variety of algor ..."
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Cited by 23 (1 self)
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The gene regulatory network (GRN) reveals the regulatory relationships among genes and can provide a systematic understanding of molecular mechanisms underlying biological processes. The importance of computer simulations in understanding cellular processes is now widely accepted; a variety of algorithms have been developed to study these biological networks. The goal of this study is to provide a comprehensive evaluation and a practical guide to aid in choosing statistical methods for constructing large scale GRNs. Using both simulation studies and a real application in E. coli data, we compare different methods in terms of sensitivity and specificity in identifying the true connections and the hub genes, the ease of use, and computational speed. Our results show that these algorithms performed reasonably well, and each method has its own advantages: (1) GeneNet, WGCNA (Weighted Correlation Network Analysis), and ARACNE (Algorithm for the Reconstruction of Accurate Cellular Networks) performed well in constructing the global network structure; (2) GeneNet and SPACE (Sparse PArtial Correlation Estimation) performed well in identifying a few connections with high specificity.