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Random Algorithms for the Loop Cutset Problem
 Journal of Artificial Intelligence Research
, 1999
"... We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called RepeatedWGuessI, outputs a minimum loop cutset, after O(c ..."
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Cited by 81 (2 self)
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We show how to find a minimum loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in Pearl's method of conditioning for inference. Our random algorithm for finding a loop cutset, called RepeatedWGuessI, outputs a minimum loop cutset, after O(c \Delta 6 k kn) steps, with probability at least 1 \Gamma (1 \Gamma 1 6 k ) c6 k , where c ? 1 is a constant specified by the user, k is the size of a minimum weight loop cutset, and n is the number of vertices. We also show empirically that a variant of this algorithm, called WRA, often finds a loop cutset that is closer to the minimum loop cutset than the ones found by the best deterministic algorithms known. 1
Faster sequential genetic linkage computations
 AMERICAN JOURNAL OF HUMAN GENETICS
, 1993
"... Linkage analysis using maximum likelihood estimation is a powerful tool for locating genes. As available data sets have grown, the computation required for analysis has grown exponentially, and become a significant impediment. Others have previously shown that parallel computation is applicable to l ..."
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Cited by 36 (1 self)
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Linkage analysis using maximum likelihood estimation is a powerful tool for locating genes. As available data sets have grown, the computation required for analysis has grown exponentially, and become a significant impediment. Others have previously shown that parallel computation is applicable to linkage analysis and can yield order of magnitude improvements in speed. In this paper, we demonstrate that algorithmic modifications can also yield order of magnitude improvements, and sometimes much more. Using the software package LINKAGE, we describe a variety of algorithmic improvements we have implemented, demonstrating how these techniques are applied, and their power. Experiments show that these improvements speed up the programs by an order of magnitude on problems of moderate and large size. All improvements were made only in the combinatorial part of the code, without resorting to parallel computers. These improvements synthesize biological principles with computer science techniques to effectively restructure the timeconsuming computations in genetic linkage analysis.
Graphical Models for Genetic Analyses
 STATISTTICAL SCIENCE
, 2003
"... This paper introduces graphical models as a natural environment in which to formulate and solve problems in genetics and related areas. Particular emphasis is given to the relationships among various local computation algorithms which have been developed within the hitherto mostly separate areas o ..."
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Cited by 28 (0 self)
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This paper introduces graphical models as a natural environment in which to formulate and solve problems in genetics and related areas. Particular emphasis is given to the relationships among various local computation algorithms which have been developed within the hitherto mostly separate areas of graphical models and genetics. The potential of graphical models is explored and illustrated through a number of example applications where the genetic element is substantial or dominating.
Online system for faster multipoint linkage analysis via parallel execution on thousands of personal computers
 American Journal of Human Genetics
"... Computation of LOD scores is a valuable tool for mapping diseasesusceptibility genes in the study of Mendelian and complex diseases. However, computation of exact multipoint likelihoods of large inbred pedigrees with extensive missing data is often beyond the capabilities of a single computer. We p ..."
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Cited by 9 (2 self)
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Computation of LOD scores is a valuable tool for mapping diseasesusceptibility genes in the study of Mendelian and complex diseases. However, computation of exact multipoint likelihoods of large inbred pedigrees with extensive missing data is often beyond the capabilities of a single computer. We present a distributed system called “SUPERLINKONLINE, ” for the computation of multipoint LOD scores of large inbred pedigrees. It achieves high performance via the efficient parallelization of the algorithms in SUPERLINK, a stateoftheart serial program for these tasks, and through the use of the idle cycles of thousands of personal computers. The main algorithmic challenge has been to efficiently split a large task for distributed execution in a highly dynamic, nondedicated running environment. Notably, the system is available online, which allows computationally intensive analyses to be performed with no need for either the installation of software or the maintenance of a complicated distributed environment. As the system was being developed, it was extensively tested by collaborating medical centers worldwide on a variety of real data sets, some of which are presented in this article. Computation of LOD is a valuable tool for mapping diseasesusceptibility genes in the study of Mendelian and complex diseases. Computation of the LOD score— defined as log 10 (L HA/L H0) , where LH0
Multilocus linkage analysis by blocked Gibbs sampling
 Statistics and Computing
, 2000
"... The problem of multilocus linkage analysis is expressed as a graphical model, making explicit a previously implicit connection, and recent developments in the field are described in this context. A novel application of blocked Gibbs sampling for Bayesian networks is developed to generate inheritance ..."
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Cited by 9 (0 self)
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The problem of multilocus linkage analysis is expressed as a graphical model, making explicit a previously implicit connection, and recent developments in the field are described in this context. A novel application of blocked Gibbs sampling for Bayesian networks is developed to generate inheritance matrices from an irreducible Markov chain. This is used as the basis for reconstruction of historical meiotic states and approximate calculation of the likelihood function for the location of an unmapped genetic trait. We believe this to be the only approach that currently makes fully informative multilocus linkage analysis possible on large extended pedigrees.
Avoiding Recomputation in Linkage Analysis
, 1994
"... We describe four improvements we have implemented in a version of the genetic linkage analysis programs in the LINKAGE package: subdivision of recombination classes, better handling of loops, better coordination between the optimization and output routines, and a checkpointing facility. The unifying ..."
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Cited by 8 (0 self)
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We describe four improvements we have implemented in a version of the genetic linkage analysis programs in the LINKAGE package: subdivision of recombination classes, better handling of loops, better coordination between the optimization and output routines, and a checkpointing facility. The unifying theme for all the improvements is to store a small amount of data to avoid expensive recomputation of known results. The subdivision of recombination classes improves on a method of Lathrop and Lalouel [Amer. J. Hum. Genetics 42(1988), pp. 498{505]. The new method of handling loops extends a proposal of Lange and Elston [Hum. Hered. 25(1975), pp. 95{105] for loopless pedigrees with multiple nuclear families at the earliest generation. From a practical point of view, the most important improvement may be the checkpointing facility which allows the user to carry out linkage computations that are much longer than the meantimetofailure of the underlying computer.
J. Dairy Sci. 85:1623–1629 © American Dairy Science Association, 2002. Technical Note: Determining Peeling Order Using Sparse Matrix Algorithms 1
"... To study the effect of individual genes by segregation or linkage analyses, the likelihood of the model needs to be evaluated. The likelihood can be computed efficiently using the ElstonStewart algorithm. This algorithm involves summing over the unobserved genotypes in the pedigree, which is called ..."
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To study the effect of individual genes by segregation or linkage analyses, the likelihood of the model needs to be evaluated. The likelihood can be computed efficiently using the ElstonStewart algorithm. This algorithm involves summing over the unobserved genotypes in the pedigree, which is called peeling. An important aspect of this algorithm is to determine the order of peeling to maximize efficiency. This paper shows how determining peeling order is related to a problem in solving systems of symmetric sparse linear equations. It also shows how algorithms developed to efficiently solve those systems, can be used to determine the optimal order of peeling in the ElstonStewart algorithm. (Key words: peeling order, sparse matrices)
THE GENETICS OF MANIC A PREDIGREE AND DEPRESSIVE ILLNESS: LINKAGE STUDY
"... A Pedigree and Linkage Study. (Under the direction of R.C. ELSTON.) A likelihood method of pedigree analysis is applied to four previously reported sets of data on manic depressive illness, and linkage analysis is performed on a large family with manic depressive illness, colorblindness and the Xg b ..."
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A Pedigree and Linkage Study. (Under the direction of R.C. ELSTON.) A likelihood method of pedigree analysis is applied to four previously reported sets of data on manic depressive illness, and linkage analysis is performed on a large family with manic depressive illness, colorblindness and the Xg blood group. Some of the problems inherent in the study of mental illnesses are alleviated in this analysis: all the information in the family structure is used, the variable age of onset is taken into account, the fact that families are ascertained via one or more probands is allowed for, and one and twogene hypotheses are tested versus a general alternative by a likelihood ratio test. Methods are given to correct for a twostage ascertainment which is sometimes used in an attempt to reduce genetic heterogeneity in a set of families. In this type of sample selection families are first ascertained through a proband in the usual way, then a subset of these families is chosen for analysis on the basis of some criterion of family history. Corrections are explicitly given for the cases in which the second stage criterion is that there are at least two affected people in the family, and that there is no fathertoson transmission of the disease. The analysis is consistent over all four sets of data, and indicates that neither a single Xlinked gene nor a single autosomal gene can account for the transmission of manic depressive illness. None of the twogene models examined were significantly more likely than the singlegene models. However, linkage analysis on a single large family gives somesuggestion that there may be a locus on. the Xchromosome closely linked to the Xg blood group which has a rare allele that can cause manic depressive illness in.an occasional family with the disease. \, \ ACKNOWLEDGEMENTS I would like to express my appreciation to my advisor, Dr. R. C. Elston, who suggested the topic of this research and provided valuable guidance. Thanks also go to the members of my committee, Drs. M.E.
Carrier Risk Calculations for Recessive Diseases when all the Mutant Alleles are not Detectable
"... There are certain recessive diseases in which some of mutations causing the disease, can be detected using the genetic probabilities. For counseling purposes, the probability that, a consultand known not to have a detectable mutation, a carrier needs to be calculated with as much accuracy as possibl ..."
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There are certain recessive diseases in which some of mutations causing the disease, can be detected using the genetic probabilities. For counseling purposes, the probability that, a consultand known not to have a detectable mutation, a carrier needs to be calculated with as much accuracy as possible. A method for the carrier risk calculation is proposed, which is based on information on the parents, one or two sibs and one or two children as well as on the spouse of the consultand in terms of positive or negative test results only, since genotype configurations for all of them may not be available in practice. For a particular disease, the carrier risk is calculated by its incidence and the proportion of the mutations that are detectable, the table once produced can be used for any family of the types included.
Summary
"... Markov chain Monte Carlo methods are frequently used in the analyses of genetic data on pedigrees for the estimation of probabilities and likelihoods which cannot be calculated by existing exact methods. In the case of discrete data, the underlying Markov chain may be reducible and care must be take ..."
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Markov chain Monte Carlo methods are frequently used in the analyses of genetic data on pedigrees for the estimation of probabilities and likelihoods which cannot be calculated by existing exact methods. In the case of discrete data, the underlying Markov chain may be reducible and care must be taken to ensure that reliable estimates are obtained. Potential reducibility thus has implications for the analysis of the mixed inheritance model, for example, where genetic variation is assumed to be due to one single locus of large effect and many loci each with a small effect. Similarly, reducibility arises in the detection of quantitative trait loci from incomplete discrete marker data. This paper aims to describe the estimation problem in terms of simple discrete genetic models and the singlesite Gibbs sampler. Reducibility of the Gibbs sampler is discussed and some current methods for circumventing the problem outlined.