title: Learning a Markov Logic network for supervised gene regulatory network inference.
abstract: BACKGROUND
  Gene regulatory network inference remains a challenging problem in systems biology despite the numerous approaches that have been proposed. When substantial knowledge on a gene regulatory network is already available, supervised network inference is appropriate. Such a method builds a binary classifier able to assign a class (Regulation/No regulation) to an ordered pair of genes. Once learnt, the pairwise classifier can be used to predict new regulations. In this work, we explore the framework of Markov Logic Networks (MLN) that combine features of probabilistic graphical models with the expressivity of first-order logic rules.
  
  
  RESULTS
  We propose to learn a Markov Logic network, e.g. a set of weighted rules that conclude on the predicate "regulates", starting from a known gene regulatory network involved in the switch proliferation/differentiation of keratinocyte cells, a set of experimental transcriptomic data and various descriptions of genes all encoded into first-order logic. As training data are unbalanced, we use asymmetric bagging to learn a set of MLNs. The prediction of a new regulation can then be obtained by averaging predictions of individual MLNs. As a side contribution, we propose three in silico tests to assess the performance of any pairwise classifier in various network inference tasks on real datasets. A first test consists of measuring the average performance on balanced edge prediction problem; a second one deals with the ability of the classifier, once enhanced by asymmetric bagging, to update a given network. Finally our main result concerns a third test that measures the ability of the method to predict regulations with a new set of genes. As expected, MLN, when provided with only numerical discretized gene expression data, does not perform as well as a pairwise SVM in terms of AUPR. However, when a more complete description of gene properties is provided by heterogeneous sources, MLN achieves the same performance as a black-box model such as a pairwise SVM while providing relevant insights on the predictions.
  
  
  CONCLUSIONS
  The numerical studies show that MLN achieves very good predictive performance while opening the door to some interpretability of the decisions. Besides the ability to suggest new regulations, such an approach allows to cross-validate experimental data with existing knowledge.
authors.affiliation: IBISC EA 4526, Université d'Évry-Val d'Essonne, 23 Boulevard de France, 91037, Évry, France. celine.brouard@ibisc.univ-evry.fr.
authors.forename: Céline
authors.initials: C
authors.lastname: Brouard
authors.forename: Christel
authors.initials: C
authors.lastname: Vrain
authors.forename: Julie
authors.initials: J
authors.lastname: Dubois
authors.forename: David
authors.initials: D
authors.lastname: Castel
authors.forename: Marie-Anne
authors.initials: MA
authors.lastname: Debily
authors.forename: Florence
authors.initials: F
authors.lastname: d'Alché-Buc
mesh_terms: D003198:Computer Simulation; D030541:Databases, Genetic; D053263:Gene Regulatory Networks; D006801:Humans; D008128:Logic; D008390:Markov Chains; D015233:Models, Statistical; D012372:ROC Curve; D060388:Support Vector Machine; D049490:Systems Biology / Q000379:methods*
references.citation: Bioinformatics. 2004 Dec 12;20(18):3565-74
references.pmid: 15284096
references.citation: Bioinformatics. 2006 Apr 1;22(7):815-22
references.pmid: 16418235
references.citation: Nucleic Acids Res. 2010 Jan;38(Database issue):D525-31
references.pmid: 19850723
references.citation: Bioinformatics. 2005 May 15;21(10):2488-95
references.pmid: 15728114
references.citation: Curr Genomics. 2009 Sep;10(6):416-29
references.pmid: 20190956
references.citation: BMC Bioinformatics. 2011 Mar 17;12:77
references.pmid: 21414208
references.citation: PLoS One. 2010 Sep 28;5(9):
references.pmid: 20927193
references.citation: PLoS Biol. 2007 Jan;5(1):e8
references.pmid: 17214507
references.citation: Pac Symp Biocomput. 2004;:300-11
references.pmid: 14992512
references.citation: BMC Bioinformatics. 2007;8 Suppl 10:S8
references.pmid: 18269702
references.citation: IEEE Trans Pattern Anal Mach Intell. 2006 Jul;28(7):1088-99
references.pmid: 16792098
references.citation: Cancer Res. 2000 Nov 1;60(21):5929-33
references.pmid: 11085505
references.citation: Bioinformatics. 2005 Jun 15;21(12):2883-90
references.pmid: 15802287
references.citation: Bioinformatics. 2004 Aug 4;20 Suppl 1:i363-70
references.pmid: 15262821
references.citation: Proc Natl Acad Sci U S A. 2005 Apr 5;102(14):4936-42
references.pmid: 15788537
references.citation: BMC Bioinformatics. 2006 Mar 20;7 Suppl 1:S7
references.pmid: 16723010
references.citation: Bioinformatics. 2003 Oct 12;19(15):1917-26
references.pmid: 14555624
references.citation: J Comput Biol. 2000;7(3-4):601-20
references.pmid: 11108481
references.citation: Nucleic Acids Res. 2011 Jan;39(Database issue):D52-7
references.pmid: 21115458
references.citation: Bioinformatics. 2005 Jan 15;21(2):218-26
references.pmid: 15319262
references.citation: Nat Genet. 2000 May;25(1):25-9
references.pmid: 10802651
references.citation: Protein Eng. 1992 Oct;5(7):647-57
references.pmid: 1480619
references.citation: Science. 2003 Jul 4;301(5629):102-5
references.pmid: 12843395
references.citation: Bioinformatics. 2008 Aug 15;24(16):i76-82
references.pmid: 18689844
references.citation: Bioinformatics. 2005 Jun;21 Suppl 1:i38-46
references.pmid: 15961482
references.citation: BMC Bioinformatics. 2013;14 Suppl 1:S3
references.pmid: 23368951
references.citation: Bioinformatics. 2007 Jul 1;23(13):i57-65
references.pmid: 17646345
references.citation: BMC Bioinformatics. 2010 Mar 25;11:154
references.pmid: 20338053
references.citation: BMC Bioinformatics. 2010 May 05;11:228
references.pmid: 20444264
references.citation: Stat Appl Genet Mol Biol. 2005;4:Article32
references.pmid: 16646851
references.citation: Biometrics. 1988 Sep;44(3):837-45
references.pmid: 3203132
references.citation: BMC Bioinformatics. 2010 Oct 19;11:520
references.pmid: 20955620