Maximum likelihood pedigree reconstruction using integer programming

Abstract Pedigrees are ‘family trees’ relating groups of individuals which can usefully be seen as Bayesian networks. The problem of finding a maximum likelihood pedigree from genotypic data is encoded as an integer linear programming problem. Two methods of ensuring that pedigrees are acyclic are considered. Results on obtaining maximum likelihood pedigrees relating 20, 46 and 59 individuals are presented. Running times for larger pedigrees depend strongly on the data used but generally compare well with those in the literature. Solving is particularly fast when allele frequency is uniform.

[1]  T Egeland,et al.  Beyond traditional paternity and identification cases. Selecting the most probable pedigree. , 2000, Forensic science international.

[2]  Peter M Vallone,et al.  Allele frequencies for 15 autosomal STR loci on U.S. Caucasian, African American, and Hispanic populations. , 2003, Journal of forensic sciences.

[3]  Anthony Almudevar,et al.  A simulated annealing algorithm for maximum likelihood pedigree reconstruction. , 2003, Theoretical population biology.

[4]  Steffen L. Lauritzen,et al.  Graphical Models for Genetic Analyses , 2003 .

[5]  Tobias Achterberg,et al.  Constraint integer programming , 2007 .

[6]  Panagiotis Manolios,et al.  Checking Pedigree Consistency with PCS , 2007, TACAS.

[7]  Anthony Almudevar,et al.  A graphical approach to relatedness inference. , 2007, Theoretical population biology.

[8]  N A Sheehan,et al.  Structured Incorporation of Prior Information in Relationship Identification Problems , 2007, Annals of human genetics.

[9]  Simon de Givry,et al.  Mendelian Error Detection in Complex Pedigrees Using Weighted Constraint Satisfaction Techniques , 2007, Constraints.

[10]  James Cussens,et al.  Bayesian network learning by compiling to weighted MAX-SAT , 2008, UAI.

[11]  Robert G Cowell,et al.  Efficient maximum likelihood pedigree reconstruction. , 2009, Theoretical population biology.

[12]  Peter F. Stadler,et al.  FRANz: reconstruction of wild multi-generation pedigrees , 2009, Bioinform..

[13]  Tommi S. Jaakkola,et al.  Learning Bayesian Network Structure using LP Relaxations , 2010, AISTATS.