Pure Parsimony Xor Haplotyping

The haplotype resolution from xor-genotype data has been recently formulated as a new model for genetic studies. The xor-genotype data is a cheaply obtainable type of data distinguishing heterozygous from homozygous sites without identifying the homozygous alleles. In this paper we propose a formulation based on a well-known model used in haplotype inference: pure parsimony. We exhibit exact solutions of the problem by providing polynomial time algorithms for some restricted cases and a fixed-parameter algorithm for the general case. These results are based on some interesting combinatorial properties of a graph representation of the solutions. Furthermore, we show that the problem has a polynomial time k-approximation, where k is the maximum number of xor-genotypes containing a given SNP. Finally, we propose a heuristic and produce an experimental analysis showing that it scales to real-world large instances taken from the HapMap project

Maximum parsimony xor haplotyping by sparse dictionary selection

Background: Xor-genotype is a cost-effective alternative to the genotype sequence of an individual. Recent methods developed for haplotype inference have aimed at finding the solution based on xor-genotype data. Given the xor-genotypes of a group of unrelated individuals, it is possible to infer the haplotype pairs for each individual with the aid of a small number of regular genotypes. Results: We propose a framework of maximum parsimony inference of haplotypes based on the search of a sparse dictionary, and we present a greedy method that can effectively infer the haplotype pairs given a set of xor-genotypes augmented by a small number of regular genotypes. We test the performance of the proposed approach on synthetic data sets with different number of individuals and SNPs, and compare the performances with the state-of-the-art xor-haplotyping methods PPXH and XOR-HAPLOGEN. Conclusions: Experimental results show good inference qualities for the proposed method under all circumstances, especially on large data sets. Results on a real database, CFTR, also demonstrate significantly better performance. The proposed algorithm is also capable of finding accurate solutions with missing data and/or typing errors

Topics in Signal Processing: applications in genomics and genetics

The information in genomic or genetic data is influenced by various complex processes and appropriate mathematical modeling is required for studying the underlying processes and the data. This dissertation focuses on the formulation of mathematical models for certain problems in genomics and genetics studies and the development of algorithms for proposing efficient solutions. A Bayesian approach for the transcription factor (TF) motif discovery is examined and the extensions are proposed to deal with many interdependent parameters of the TF-DNA binding. The problem is described by statistical terms and a sequential Monte Carlo sampling method is employed for the estimation of unknown parameters. In particular, a class-based resampling approach is applied for the accurate estimation of a set of intrinsic properties of the DNA binding sites. Through statistical analysis of the gene expressions, a motif-based computational approach is developed for the inference of novel regulatory networks in a given bacterial genome. To deal with high false-discovery rates in the genome-wide TF binding predictions, the discriminative learning approaches are examined in the context of sequence classification, and a novel mathematical model is introduced to the family of kernel-based Support Vector Machines classifiers. Furthermore, the problem of haplotype phasing is examined based on the genetic data obtained from cost-effective genotyping technologies. Based on the identification and augmentation of a small and relatively more informative genotype set, a sparse dictionary selection algorithm is developed to infer the haplotype pairs for the sampled population. In a relevant context, to detect redundant information in the single nucleotide polymorphism (SNP) sites, the problem of representative (tag) SNP selection is introduced. An information theoretic heuristic is designed for the accurate selection of tag SNPs that capture the genetic diversity in a large sample set from multiple populations. The method is based on a multi-locus mutual information measure, reflecting a biological principle in the population genetics that is linkage disequilibrium