Revealing Structure of Complex Biological Systems Using Bayesian Networks

Bayesian networks represent statistical dependencies among variables; they are able to model multiple types of relationships, including stochastic, non-linear, and arbitrary combinatoric. Such flexibility has made them excellent models for reverse-engineering structure of complex networks. This chapter reviews the use of Bayesian networks for probing structure of biological systems. We begin with an introduction to Bayesian networks, addressing especially issues of their interpretation as relates to understanding system structure. We then cover how Bayesian network structures are learned from data, considering a popular scoring metric, the BDe, in detail. We finish by reviewing the uses of Bayesian networks in biological systems to date and the concurrent advances in Bayesian network methodology tailored for use in biology.

[1]  Gregory F. Cooper,et al.  Causal Discovery from a Mixture of Experimental and Observational Data , 1999, UAI.

[2]  Dimitris Samaras,et al.  Modeling Neuronal Interactivity using Dynamic Bayesian Networks , 2005, NIPS.

[3]  David Heckerman,et al.  A Tutorial on Learning with Bayesian Networks , 1999, Innovations in Bayesian Networks.

[4]  Dimitris Margaritis,et al.  Distribution-Free Learning of Bayesian Network Structure in Continuous Domains , 2005, AAAI.

[5]  Rong Jin,et al.  On the Use of Dynamic Bayesian Networks in Reconstructing Functional Neuronal Networks from Spike Train Ensembles , 2010, Neural Computation.

[6]  Tommi S. Jaakkola,et al.  Combining Location and Expression Data for Principled Discovery of Genetic Regulatory Network Models , 2001, Pacific Symposium on Biocomputing.

[7]  Nir Friedman,et al.  Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks , 2004, Machine Learning.

[8]  N. L. Johnson,et al.  Continuous Multivariate Distributions: Models and Applications , 2005 .

[9]  Akhilesh Pandey,et al.  Comparisons of tyrosine phosphorylated proteins in cells expressing lung cancer-specific alleles of EGFR and KRAS , 2008, Proceedings of the National Academy of Sciences.

[10]  Nir Friedman,et al.  Inferring subnetworks from perturbed expression profiles , 2001, ISMB.

[11]  T. Dawson,et al.  Predicting the impacts of climate change on the distribution of species: are bioclimate envelope models useful? , 2003 .

[12]  Sascha Ott,et al.  Increasing feasibility of optimal gene network estimation. , 2004, Genome informatics. International Conference on Genome Informatics.

[13]  Paul P. Wang,et al.  Advances to Bayesian network inference for generating causal networks from observational biological data , 2004, Bioinform..

[14]  F Matthäus,et al.  Interactive Molecular Networks Obtained by Computer-aided Conversion of Microarray Data from Brains of Alcohol-drinking Rats , 2009, Pharmacopsychiatry.

[15]  Vincent Frouin,et al.  Evolutionary approaches for the reverse-engineering of gene regulatory networks: A study on a biologically realistic dataset , 2008, BMC Bioinformatics.

[16]  Kevin Murphy,et al.  Modelling Gene Expression Data using Dynamic Bayesian Networks , 2006 .

[17]  A. Arkin,et al.  Stochastic mechanisms in gene expression. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[18]  John Quackenbush,et al.  Seeded Bayesian Networks: Constructing genetic networks from microarray data , 2008, BMC Systems Biology.

[19]  Deborah Sanders,et al.  Computational Strategy for Discovering Druggable Gene Networks from Genome-Wide RNA Expression Profiles , 2005, Pacific Symposium on Biocomputing.

[20]  Karim Oweiss,et al.  Reconstructing functional neuronal circuits using dynamic Bayesian networks , 2008, 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[21]  Henry Tirri,et al.  B-Course: A Web-Based Tool for Bayesian and Causal Data Analysis , 2002, Int. J. Artif. Intell. Tools.

[22]  Satoru Miyano,et al.  Bayesian Network and Nonparametric Heteroscedastic Regression for Nonlinear Modeling of Genetic Network , 2003, J. Bioinform. Comput. Biol..

[23]  Robert G. Cowell,et al.  Conditions Under Which Conditional Independence and Scoring Methods Lead to Identical Selection of Bayesian Network Models , 2001, UAI.

[24]  Bartek Wilczynski,et al.  BNFinder: exact and efficient method for learning Bayesian networks , 2008, Bioinform..

[25]  V. Anne Smith,et al.  Influence of Network Topology and Data Collection on Network Inference , 2003, Pacific Symposium on Biocomputing.

[26]  Amos Tanay,et al.  Minreg: Inferring an active regulator set , 2002, ISMB.

[27]  W. G. Kelly,et al.  Functional genomic analysis of the ADP‐ribosylation factor family of GTPases: phylogeny among diverse eukaryotes and function in C. elegans , 2004, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[28]  Tianzi Jiang,et al.  Exploring candidate genes for human brain diseases from a brain-specific gene network. , 2006, Biochemical and biophysical research communications.

[29]  Satoru Miyano,et al.  Combining Microarrays and Biological Knowledge for Estimating Gene Networks via Bayesian Networks , 2004, J. Bioinform. Comput. Biol..

[30]  David Maxwell Chickering,et al.  Learning Bayesian Networks is NP-Complete , 2016, AISTATS.

[31]  Giovanni Fusco Looking for sustainable urban mobility through bayesian network , 2003 .

[32]  Claus Dethlefsen,et al.  deal: A Package for Learning Bayesian Networks , 2003 .

[33]  Tommi S. Jaakkola,et al.  Using Graphical Models and Genomic Expression Data to Statistically Validate Models of Genetic Regulatory Networks , 2000, Pacific Symposium on Biocomputing.

[34]  D. A. Kenny,et al.  Correlation and Causation , 1937, Wilmott.

[35]  Martin J. McKeown,et al.  Bayesian Network Modeling for Discovering “Dependent Synergies” Among Muscles in Reaching Movements , 2008, IEEE Transactions on Biomedical Engineering.

[36]  Juan Zhou,et al.  Learning effective brain connectivity with dynamic Bayesian networks , 2007, NeuroImage.

[37]  P. Bandettini,et al.  What's New in Neuroimaging Methods? , 2009, Annals of the New York Academy of Sciences.

[38]  Rong Jin,et al.  Inferring functional cortical networks from spike train ensembles using Dynamic Bayesian Networks , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[39]  Gregory F. Cooper,et al.  Discovery of Causal Relationships in a Gene-Regulation Pathway from a Mixture of Experimental and Observational DNA Microarray Data , 2001, Pacific Symposium on Biocomputing.

[40]  Guoliang Xue,et al.  Applying two-level simulated annealing on Bayesian structure learning to infer genetic networks , 2004 .

[41]  N. L. Johnson,et al.  Continuous Multivariate Distributions, Volume 1: Models and Applications , 2019 .

[42]  Tommi S. Jaakkola,et al.  On the Dirichlet Prior and Bayesian Regularization , 2002, NIPS.

[43]  P. Spirtes,et al.  An Algorithm for Fast Recovery of Sparse Causal Graphs , 1991 .

[44]  Michael I. Jordan,et al.  Learning Graphical Models with Mercer Kernels , 2002, NIPS.

[45]  J. Derisi,et al.  A Bayesian Network Driven Approach to Model the Transcriptional Response to Nitric Oxide in Saccharomyces cerevisiae , 2006, PloS one.

[46]  David J. Spiegelhalter,et al.  Bayesian analysis in expert systems , 1993 .

[47]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[48]  Michal Linial,et al.  Using Bayesian Networks to Analyze Expression Data , 2000, J. Comput. Biol..

[49]  Satoru Miyano,et al.  Estimation of Genetic Networks and Functional Structures Between Genes by Using Bayesian Networks and Nonparametric Regression , 2001, Pacific Symposium on Biocomputing.

[50]  Xiaohui Chen,et al.  BNArray: an R package for constructing gene regulatory networks from microarray data by using Bayesian network. , 2006, Bioinformatics.

[51]  Alexander J. Hartemink,et al.  Informative Structure Priors: Joint Learning of Dynamic Regulatory Networks from Multiple Types of Data , 2004, Pacific Symposium on Biocomputing.

[52]  Satoru Miyano,et al.  Identifying drug active pathways from gene networks estimated by gene expression data. , 2005, Genome informatics. International Conference on Genome Informatics.

[53]  Carlos Cotta,et al.  A Primer on the Evolution of Equivalence Classes of Bayesian-Network Structures , 2004, PPSN.

[54]  Dirk Husmeier,et al.  Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks , 2003, Bioinform..

[55]  Rainer Spang,et al.  Inferring cellular networks – a review , 2007, BMC Bioinformatics.

[56]  Satoru Miyano,et al.  Estimating gene networks from gene expression data by combining Bayesian network model with promoter element detection , 2003, ECCB.

[57]  Patrick C Phillips,et al.  Network thinking in ecology and evolution. , 2005, Trends in ecology & evolution.

[58]  K. Sachs,et al.  Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data , 2005, Science.

[59]  Nir Friedman,et al.  Inferring Cellular Networks Using Probabilistic Graphical Models , 2004, Science.

[60]  Jing Yu,et al.  Developing bayesian network inference algorithms to predict causal functional pathways in biological systems , 2005 .

[61]  Wai Lam,et al.  LEARNING BAYESIAN BELIEF NETWORKS: AN APPROACH BASED ON THE MDL PRINCIPLE , 1994, Comput. Intell..

[62]  Doheon Lee,et al.  Modularized learning of genetic interaction networks from biological annotations and mRNA expression data , 2005, Bioinform..

[63]  J. Lawton,et al.  Making mistakes when predicting shifts in species range in response to global warming , 1998, Nature.

[64]  Colin M Beale,et al.  Revealing ecological networks using Bayesian network inference algorithms. , 2010, Ecology.

[65]  David Page,et al.  Modelling regulatory pathways in E. coli from time series expression profiles , 2002, ISMB.

[66]  V. Anne Smith,et al.  Causal pattern recovery from neural spike train data using the Snap Shot Score , 2010, Journal of Computational Neuroscience.

[67]  C. Knight,et al.  Pale Rock Sparrow Carpospiza brachydactyla in the Mount Lebanon range: modelling breeding habitat , 2005 .

[68]  Mingyi Wang,et al.  A hybrid Bayesian network learning method for constructing gene networks , 2007, Comput. Biol. Chem..

[69]  D. Husmeier,et al.  Reconstructing Gene Regulatory Networks with Bayesian Networks by Combining Expression Data with Multiple Sources of Prior Knowledge , 2007, Statistical applications in genetics and molecular biology.

[70]  Satoru Miyano,et al.  Utilizing Evolutionary Information and Gene Expression Data for Estimating Gene Networks with Bayesian Network Models , 2005, J. Bioinform. Comput. Biol..

[71]  Jing Yu,et al.  Computational Inference of Neural Information Flow Networks , 2006, PLoS Comput. Biol..

[72]  Wray L. Buntine Theory Refinement on Bayesian Networks , 1991, UAI.

[73]  Quentin Paynter,et al.  The invertebrate fauna on broom, Cytisus scoparius, in two native and two exotic habitats , 2000 .

[74]  Weiru Liu,et al.  Learning belief networks from data: an information theory based approach , 1997, CIKM '97.

[75]  Satoru Miyano,et al.  Using Protein-Protein Interactions for Refining Gene Networks Estimated from Microarray Data by Bayesian Networks , 2003, Pacific Symposium on Biocomputing.

[76]  Rajesh P. N. Rao Bayesian Computation in Recurrent Neural Circuits , 2004, Neural Computation.

[77]  Kevin B. Korb,et al.  Causal Discovery via MML , 1996, ICML.

[78]  Jagath C. Rajapakse,et al.  Learning functional structure from fMR images , 2006, NeuroImage.

[79]  Uri T Eden,et al.  A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. , 2005, Journal of neurophysiology.

[80]  N. Wermuth,et al.  Graphical and recursive models for contingency tables , 1983 .

[81]  Joe Suzuki,et al.  A Construction of Bayesian Networks from Databases Based on an MDL Principle , 1993, UAI.

[82]  Aurélien Mazurie,et al.  Gene networks inference using dynamic Bayesian networks , 2003, ECCB.

[83]  Bartek Wilczynski,et al.  Applying dynamic Bayesian networks to perturbed gene expression data , 2006, BMC Bioinformatics.

[84]  Benjamin F. Grewe,et al.  Optical probing of neuronal ensemble activity , 2009, Current Opinion in Neurobiology.

[85]  Doug Fisher,et al.  Learning from Data: Artificial Intelligence and Statistics V , 1996 .

[86]  Koichi Sameshima,et al.  Using partial directed coherence to describe neuronal ensemble interactions , 1999, Journal of Neuroscience Methods.

[87]  Hamilton E. Link,et al.  Discrete dynamic Bayesian network analysis of fMRI data , 2009, Human brain mapping.

[88]  Charles Twardy,et al.  Missing Person Behaviour An Australian Study , 2006 .

[89]  Radhakrishnan Nagarajan,et al.  NATbox: a network analysis toolbox in R , 2009, BMC Bioinformatics.

[90]  Zheng Li,et al.  Inferring pathways and networks with a Bayesian framework , 2004, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[91]  Doheon Lee,et al.  Inference of combinatorial neuronal synchrony with Bayesian networks , 2010, Journal of Neuroscience Methods.

[92]  Kevin P. Murphy,et al.  Learning the Structure of Dynamic Probabilistic Networks , 1998, UAI.

[93]  Kevin Murphy,et al.  Bayes net toolbox for Matlab , 1999 .

[94]  Nir Friedman,et al.  Learning Belief Networks in the Presence of Missing Values and Hidden Variables , 1997, ICML.

[95]  T. Speed,et al.  Recursive causal models , 1984, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[96]  Gregory T. A. Kovacs,et al.  Optical Scanner for Immunoassays With Up-Converting Phosphorescent Labels , 2008, IEEE Transactions on Biomedical Engineering.

[97]  Isabel M. Tienda-Luna,et al.  Uncovering Gene Regulatory Networks from Time-Series Microarray Data with Variational Bayesian Structural Expectation Maximization , 2007, EURASIP J. Bioinform. Syst. Biol..

[98]  Nir Friedman,et al.  Being Bayesian about Network Structure , 2000, UAI.

[99]  Xiaoyu Chen,et al.  Prediction of tissue-specific cis-regulatory modules using Bayesian networks and regression trees , 2007, BMC Bioinformatics.

[100]  Gregory F. Cooper,et al.  A Bayesian method for the induction of probabilistic networks from data , 1992, Machine Learning.