Technical Note: Computing Strategies in Genome-Wide Selection
Genome-wide genetic evaluation might involve the computation of BLUP-like estimations, potentially including thousands of covariates (i.e., single-nucleotide polymorphism markers) for each record. This implies dense Henderson's mixed-model equations and considerable computing resources in time...
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| Vydáno v: | Journal of dairy science Ročník 91; číslo 1; s. 360 - 366 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Savoy, IL
Elsevier Inc
01.01.2008
American Dairy Science Association Am Dairy Sci Assoc |
| Témata: | |
| ISSN: | 0022-0302, 1525-3198, 1525-3198 |
| On-line přístup: | Získat plný text |
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| Abstract | Genome-wide genetic evaluation might involve the computation of BLUP-like estimations, potentially including thousands of covariates (i.e., single-nucleotide polymorphism markers) for each record. This implies dense Henderson's mixed-model equations and considerable computing resources in time and storage, even for a few thousand records. Possible computing options include the type of storage and the solving algorithm. This work evaluated several computing options, including half-stored Cholesky decomposition, Gauss-Seidel, and 3 matrix-free strategies: Gauss-Seidel, Gauss-Seidel with residuals update, and preconditioned conjugate gradients. Matrix-free Gauss-Seidel with residuals update adjusts the residuals after computing the solution for each effect. This avoids adjusting the left-hand side of the equations by all other effects at every step of the algorithm and saves considerable computing time. Any Gauss-Seidel algorithm can easily be extended for variance component estimation by Markov chain-Monte Carlo. Let m and n be the number of records and markers, respectively. Computing time for Cholesky decomposition is proportional to n3. Computing times per round are proportional to mn2 in matrix-free Gauss-Seidel, to n2 for half-stored Gauss-Seidel, and to n and m for the rest of the algorithms. Algorithms were tested on a real mouse data set, which included 1,928 records and 10,946 single-nucleotide polymorphism markers. Computing times were in the order of a few minutes for Gauss-Seidel with residuals update and preconditioned conjugate gradients, more than 1h for half-stored Gauss-Seidel, 2h for Cholesky decomposition, and 4 d for matrix-free Gauss-Seidel. Preconditioned conjugate gradients was the fastest. Gauss-Seidel with residuals update would be the method of choice for variance component estimation as well as solving. |
|---|---|
| AbstractList | Genome-wide genetic evaluation might involve the computation of BLUP-like estimations, potentially including thousands of covariates (i.e., single-nucleotide polymorphism markers) for each record. This implies dense Henderson's mixed-model equations and considerable computing resources in time and storage, even for a few thousand records. Possible computing options include the type of storage and the solving algorithm. This work evaluated several computing options, including half-stored Cholesky decomposition, Gauss-Seidel, and 3 matrix-free strategies: Gauss-Seidel, Gauss-Seidel with residuals update, and preconditioned conjugate gradients. Matrix-free Gauss-Seidel with residuals update adjusts the residuals after computing the solution for each effect. This avoids adjusting the left-hand side of the equations by all other effects at every step of the algorithm and saves considerable computing time. Any Gauss-Seidel algorithm can easily be extended for variance component estimation by Markov chain-Monte Carlo. Let m and n be the number of records and markers, respectively. Computing time for Cholesky decomposition is proportional to n³. Computing times per round are proportional to mn² in matrix-free Gauss-Seidel, to n² for half-stored Gauss-Seidel, and to n and m for the rest of the algorithms. Algorithms were tested on a real mouse data set, which included 1,928 records and 10,946 single-nucleotide polymorphism markers. Computing times were in the order of a few minutes for Gauss-Seidel with residuals update and preconditioned conjugate gradients, more than 1 h for half-stored Gauss-Seidel, 2 h for Cholesky decomposition, and 4 d for matrix-free Gauss-Seidel. Preconditioned conjugate gradients was the fastest. Gauss-Seidel with residuals update would be the method of choice for variance component estimation as well as solving. Genome-wide genetic evaluation might involve the computation of BLUP-like estimations, potentially including thousands of covariates (i.e., single-nucleotide polymorphism markers) for each record. This implies dense Henderson's mixed-model equations and considerable computing resources in time and storage, even for a few thousand records. Possible computing options include the type of storage and the solving algorithm. This work evaluated several computing options, including half-stored Cholesky decomposition, Gauss-Seidel, and 3 matrix-free strategies: Gauss-Seidel, Gauss-Seidel with residuals update, and preconditioned conjugate gradients. Matrix-free Gauss-Seidel with residuals update adjusts the residuals after computing the solution for each effect. This avoids adjusting the left-hand side of the equations by all other effects at every step of the algorithm and saves considerable computing time. Any Gauss-Seidel algorithm can easily be extended for variance component estimation by Markov chain-Monte Carlo. Let m and n be the number of records and markers, respectively. Computing time for Cholesky decomposition is proportional to n3. Computing times per round are proportional to mn2 in matrix-free Gauss-Seidel, to n2 for half-stored Gauss-Seidel, and to n and m for the rest of the algorithms. Algorithms were tested on a real mouse data set, which included 1,928 records and 10,946 single-nucleotide polymorphism markers. Computing times were in the order of a few minutes for Gauss-Seidel with residuals update and preconditioned conjugate gradients, more than 1 h for half-stored Gauss-Seidel, 2 h for Cholesky decomposition, and 4 d for matrix-free Gauss-Seidel. Preconditioned conjugate gradients was the fastest. Gauss-Seidel with residuals update would be the method of choice for variance component estimation as well as solving. Genome-wide genetic evaluation might involve the computation of BLUP-like estimations, potentially including thousands of covariates (i.e., single-nucleotide polymorphism markers) for each record. This implies dense Henderson's mixed-model equations and considerable computing resources in time and storage, even for a few thousand records. Possible computing options include the type of storage and the solving algorithm. This work evaluated several computing options, including half-stored Cholesky decomposition, Gauss-Seidel, and 3 matrix-free strategies: Gauss-Seidel, Gauss-Seidel with residuals update, and preconditioned conjugate gradients. Matrix-free Gauss-Seidel with residuals update adjusts the residuals after computing the solution for each effect. This avoids adjusting the left-hand side of the equations by all other effects at every step of the algorithm and saves considerable computing time. Any Gauss-Seidel algorithm can easily be extended for variance component estimation by Markov chain-Monte Carlo. Let m and n be the number of records and markers, respectively. Computing time for Cholesky decomposition is proportional to n super(3). Computing times per round are proportional to mn super(2) in matrix-free Gauss-Seidel, to n super(2) for half-stored Gauss-Seidel, and to n and m for the rest of the algorithms. Algorithms were tested on a real mouse data set, which included 1,928 records and 10,946 single-nucleotide polymorphism markers. Computing times were in the order of a few minutes for Gauss-Seidel with residuals update and preconditioned conjugate gradients, more than 1 h for half-stored Gauss-Seidel, 2 h for Cholesky decomposition, and 4 d for matrix-free Gauss-Seidel. Preconditioned conjugate gradients was the fastest. Gauss-Seidel with residuals update would be the method of choice for variance component estimation as well as solving. Genome-wide genetic evaluation might involve the computation of BLUP-like estimations, potentially including thousands of covariates (i.e., single-nucleotide polymorphism markers) for each record. This implies dense Henderson's mixed-model equations and considerable computing resources in time and storage, even for a few thousand records. Possible computing options include the type of storage and the solving algorithm. This work evaluated several computing options, including half-stored Cholesky decomposition, Gauss-Seidel, and 3 matrix-free strategies: Gauss-Seidel, Gauss-Seidel with residuals update, and preconditioned conjugate gradients. Matrix-free Gauss-Seidel with residuals update adjusts the residuals after computing the solution for each effect. This avoids adjusting the left-hand side of the equations by all other effects at every step of the algorithm and saves considerable computing time. Any Gauss-Seidel algorithm can easily be extended for variance component estimation by Markov chain-Monte Carlo. Let m and n be the number of records and markers, respectively. Computing time for Cholesky decomposition is proportional to n3. Computing times per round are proportional to mn2 in matrix-free Gauss-Seidel, to n2 for half-stored Gauss-Seidel, and to n and m for the rest of the algorithms. Algorithms were tested on a real mouse data set, which included 1,928 records and 10,946 single-nucleotide polymorphism markers. Computing times were in the order of a few minutes for Gauss-Seidel with residuals update and preconditioned conjugate gradients, more than 1 h for half-stored Gauss-Seidel, 2 h for Cholesky decomposition, and 4 d for matrix-free Gauss-Seidel. Preconditioned conjugate gradients was the fastest. Gauss-Seidel with residuals update would be the method of choice for variance component estimation as well as solving.Genome-wide genetic evaluation might involve the computation of BLUP-like estimations, potentially including thousands of covariates (i.e., single-nucleotide polymorphism markers) for each record. This implies dense Henderson's mixed-model equations and considerable computing resources in time and storage, even for a few thousand records. Possible computing options include the type of storage and the solving algorithm. This work evaluated several computing options, including half-stored Cholesky decomposition, Gauss-Seidel, and 3 matrix-free strategies: Gauss-Seidel, Gauss-Seidel with residuals update, and preconditioned conjugate gradients. Matrix-free Gauss-Seidel with residuals update adjusts the residuals after computing the solution for each effect. This avoids adjusting the left-hand side of the equations by all other effects at every step of the algorithm and saves considerable computing time. Any Gauss-Seidel algorithm can easily be extended for variance component estimation by Markov chain-Monte Carlo. Let m and n be the number of records and markers, respectively. Computing time for Cholesky decomposition is proportional to n3. Computing times per round are proportional to mn2 in matrix-free Gauss-Seidel, to n2 for half-stored Gauss-Seidel, and to n and m for the rest of the algorithms. Algorithms were tested on a real mouse data set, which included 1,928 records and 10,946 single-nucleotide polymorphism markers. Computing times were in the order of a few minutes for Gauss-Seidel with residuals update and preconditioned conjugate gradients, more than 1 h for half-stored Gauss-Seidel, 2 h for Cholesky decomposition, and 4 d for matrix-free Gauss-Seidel. Preconditioned conjugate gradients was the fastest. Gauss-Seidel with residuals update would be the method of choice for variance component estimation as well as solving. Genome-wide genetic evaluation might involve the computation of BLUP-like estimations, potentially including thousands of covariates (i.e., single-nucleotide polymorphism markers) for each record. This implies dense Henderson's mixed-model equations and considerable computing resources in time and storage, even for a few thousand records. Possible computing options include the type of storage and the solving algorithm. This work evaluated several computing options, including half-stored Cholesky decomposition, Gauss-Seidel, and 3 matrix-free strategies: Gauss-Seidel, Gauss-Seidel with residuals update, and preconditioned conjugate gradients. Matrix-free Gauss-Seidel with residuals update adjusts the residuals after computing the solution for each effect. This avoids adjusting the left-hand side of the equations by all other effects at every step of the algorithm and saves considerable computing time. Any Gauss-Seidel algorithm can easily be extended for variance component estimation by Markov chain-Monte Carlo. Let m and n be the number of records and markers, respectively. Computing time for Cholesky decomposition is proportional to n3. Computing times per round are proportional to mn2 in matrix-free Gauss-Seidel, to n2 for half-stored Gauss-Seidel, and to n and m for the rest of the algorithms. Algorithms were tested on a real mouse data set, which included 1,928 records and 10,946 single-nucleotide polymorphism markers. Computing times were in the order of a few minutes for Gauss-Seidel with residuals update and preconditioned conjugate gradients, more than 1h for half-stored Gauss-Seidel, 2h for Cholesky decomposition, and 4 d for matrix-free Gauss-Seidel. Preconditioned conjugate gradients was the fastest. Gauss-Seidel with residuals update would be the method of choice for variance component estimation as well as solving. |
| Author | Legarra, A Misztal, I |
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| Cites_doi | 10.3168/jds.S0022-0302(87)80063-2 10.1023/A:1011094131273 10.1038/ng1840 10.3168/jds.S0022-0302(99)75536-0 10.1093/genetics/157.4.1819 10.3168/jds.S0022-0302(99)75535-9 10.2527/2001.7951166x 10.1186/1297-9686-28-1-121 |
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| Copyright | 2008 American Dairy Science Association 2008 INIST-CNRS Copyright American Dairy Science Association Jan 2008 Distributed under a Creative Commons Attribution 4.0 International License |
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| Keywords | genomic selection marker-assisted selection genetic evaluation genome-wide selection Evaluation Genomics Dairy industry Marker assisted selection Genetics Strategy Computing Genome Genome-wide selection, genomic selection, genetic evaluation, marker-assisted selection |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Agricultural sciences Algorithms Animal productions Animals artificial selection Biological and medical sciences Body Weight cattle Cholesky decomposition Computational Biology Computational Biology - methods computer software covariance equations Female Food industries Fundamental and applied biological sciences. Psychology Gauss-Seidel Gauss-Seidel with residuals update genetic evaluation genetic markers genome genome-wide selection genomic selection genomics Genomics - methods Life Sciences Male marker-assisted selection mathematical models matrix free Gauss-Seidel methods Mice Milk and cheese industries. Ice creams Models, Genetic Polymorphism, Single Nucleotide preconditioned conjugate gradients selection criteria single nucleotide polymorphism Terrestrial animal productions variance Vertebrates |
| Title | Technical Note: Computing Strategies in Genome-Wide Selection |
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