title: Bag of Naïve Bayes: biomarker selection and classification from genome-wide SNP data.
abstract: BACKGROUND
  Multifactorial diseases arise from complex patterns of interaction between a set of genetic traits and the environment. To fully capture the genetic biomarkers that jointly explain the heritability component of a disease, thus, all SNPs from a genome-wide association study should be analyzed simultaneously.
  
  
  RESULTS
  In this paper, we present Bag of Naïve Bayes (BoNB), an algorithm for genetic biomarker selection and subjects classification from the simultaneous analysis of genome-wide SNP data. BoNB is based on the Naïve Bayes classification framework, enriched by three main features: bootstrap aggregating of an ensemble of Naïve Bayes classifiers, a novel strategy for ranking and selecting the attributes used by each classifier in the ensemble and a permutation-based procedure for selecting significant biomarkers, based on their marginal utility in the classification process. BoNB is tested on the Wellcome Trust Case-Control study on Type 1 Diabetes and its performance is compared with the ones of both a standard Naïve Bayes algorithm and HyperLASSO, a penalized logistic regression algorithm from the state-of-the-art in simultaneous genome-wide data analysis.
  
  
  CONCLUSIONS
  The significantly higher classification accuracy obtained by BoNB, together with the significance of the biomarkers identified from the Type 1 Diabetes dataset, prove the effectiveness of BoNB as an algorithm for both classification and biomarker selection from genome-wide SNP data.
  
  
  BACKGROUND
  Source code of the BoNB algorithm is released under the GNU General Public Licence and is available at http://www.dei.unipd.it/~sambofra/bonb.html.
authors.affiliation: Department of Information Engineering, University of Padova, 35131 Padova, Italy.
authors.forename: Francesco
authors.initials: F
authors.lastname: Sambo
authors.forename: Emanuele
authors.initials: E
authors.lastname: Trifoglio
authors.forename: Barbara
authors.initials: B
authors.lastname: Di Camillo
authors.forename: Gianna M
authors.initials: GM
authors.lastname: Toffolo
authors.forename: Claudio
authors.initials: C
authors.lastname: Cobelli
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D016022:Case-Control Studies; D003922:Diabetes Mellitus, Type 1 / Q000235:genetics*; D005260:Female; D005819:Genetic Markers; D055106:Genome-Wide Association Study; D006801:Humans; D016015:Logistic Models; D020641:Polymorphism, Single Nucleotide
chemical_list: D005819:Genetic Markers