Bayesian network learning with cutting planes

The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of cutting planes. Finding good cutting planes is the key to the success of the approach -the search for such cutting planes is effected using a sub-IP. Results show that this is a particularly fast method for exact BN learning

A simple greedy algorithm for reconstructing pedigrees

This paper introduces a simple greedy algorithm for searching for high likelihood pedigrees using micro-satellite (STR) genotype information on a complete sample of related individuals. The core idea behind the algorithm is not new, but it is believed that putting it into a greedy search setting, and specifically the application to pedigree learning, is novel. The algorithm does not require age or sex information, but this information can be incorporated if desired. The algorithm is applied to human and non-human genetic data and in a simulation study

Efficient maximum likelihood pedigree reconstruction

A simple and efficient algorithm is presented for finding a maximum likelihood pedigree using microsatellite (STR) genotype information on a complete sample of related individuals. The computational complexity of the algorithm is at worst (O(n32n)), where n is the number of individuals. Thus it is possible to exhaustively search the space of all pedigrees of up to thirty individuals for one that maximizes the likelihood. A priori age and sex information can be used if available, but is not essential. The algorithm is applied in a simulation study, and to some real data on humans

Rapid haplotype inference for nuclear families

Hapi is a new dynamic programming algorithm that ignores uninformative states and state transitions in order to efficiently compute minimum-recombinant and maximum likelihood haplotypes. When applied to a dataset containing 103 families, Hapi performs 3.8 and 320 times faster than state-of-the-art algorithms. Because Hapi infers both minimum-recombinant and maximum likelihood haplotypes and applies to related individuals, the haplotypes it infers are highly accurate over extended genomic distances.National Institutes of Health (U.S.) (NIH grant 5-T90-DK070069)National Institutes of Health (U.S.) (Grant 5-P01-NS055923)National Science Foundation (U.S.) (Graduate Research Fellowship

A rapid conditional enumeration haplotyping method in pedigrees

Haplotyping in pedigrees provides valuable information for genetic studies (e.g., linkage analysis and association study). In order to identify a set of haplotype configurations with the highest likelihoods for a large pedigree with a large number of linked loci, in our previous work, we proposed a conditional enumeration haplotyping method which sets a threshold for the conditional probabilities of the possible ordered genotypes at every unordered individual-marker to delete some ordered genotypes with low conditional probabilities and then eliminate some haplotype configurations with low likelihoods. In this article we present a rapid haplotyping algorithm based on a modification of our previous method by setting an additional threshold for the ratio of the conditional probability of a haplotype configuration to the largest conditional probability of all haplotype configurations in order to eliminate those configurations with relatively low conditional probabilities. The new algorithm is much more efficient than our previous method and the widely used software SimWalk2

Advances in Learning Bayesian Networks of Bounded Treewidth

This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sampling $k$-trees (maximal graphs of treewidth $k$), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that $k$-tree. Some properties of these methods are discussed and proven. The approaches are empirically compared to each other and to a state-of-the-art method for learning bounded treewidth structures on a collection of public data sets with up to 100 variables. The experiments show that our exact algorithm outperforms the state of the art, and that the approximate approach is fairly accurate.Comment: 23 pages, 2 figures, 3 table