The gradient boosting algorithm and random boosting for genome-assisted evaluation in large data sets.

In the next few years, with the advent of high-density single nucleotide polymorphism (SNP) arrays and genome sequencing, genomic evaluation methods will need to deal with a large number of genetic variants and an increasing sample size. The boosting algorithm is a machine-learning technique that may alleviate the drawbacks of dealing with such large data sets. This algorithm combines different predictors in a sequential manner with some shrinkage on them; each predictor is applied consecutively to the residuals from the committee formed by the previous ones to form a final prediction based on a subset of covariates. Here, a detailed description is provided and examples using a toy data set are included. A modification of the algorithm called "random boosting" was proposed to increase predictive ability and decrease computation time of genome-assisted evaluation in large data sets. Random boosting uses a random selection of markers to add a subsequent weak learner to the predictive model. These modifications were applied to a real data set composed of 1,797 bulls genotyped for 39,714 SNP. Deregressed proofs of 4 yield traits and 1 type trait from January 2009 routine evaluations were used as dependent variables. A 2-fold cross-validation scenario was implemented. Sires born before 2005 were used as a training sample (1,576 and 1,562 for production and type traits, respectively), whereas younger sires were used as a testing sample to evaluate predictive ability of the algorithm on yet-to-be-observed phenotypes. Comparison with the original algorithm was provided. The predictive ability of the algorithm was measured as Pearson correlations between observed and predicted responses. Further, estimated bias was computed as the average difference between observed and predicted phenotypes. The results showed that the modification of the original boosting algorithm could be run in 1% of the time used with the original algorithm and with negligible differences in accuracy and bias. This modification may be used to speed the calculus of genome-assisted evaluation in large data sets such us those obtained from consortiums.

González-Recio O ，Jiménez-Montero JA ，Alenda R 《-》

Comparison of methods for the implementation of genome-assisted evaluation of Spanish dairy cattle.

The aim of this study was to evaluate methods for genomic evaluation of the Spanish Holstein population as an initial step toward the implementation of routine genomic evaluations. This study provides a description of the population structure of progeny tested bulls in Spain at the genomic level and compares different genomic evaluation methods with regard to accuracy and bias. Two bayesian linear regression models, Bayes-A and Bayesian-LASSO (B-LASSO), as well as a machine learning algorithm, Random-Boosting (R-Boost), and BLUP using a realized genomic relationship matrix (G-BLUP), were compared. Five traits that are currently under selection in the Spanish Holstein population were used: milk yield, fat yield, protein yield, fat percentage, and udder depth. In total, genotypes from 1859 progeny tested bulls were used. The training sets were composed of bulls born before 2005; including 1601 bulls for production and 1574 bulls for type, whereas the testing sets contained 258 and 235 bulls born in 2005 or later for production and type, respectively. Deregressed proofs (DRP) from January 2009 Interbull (Uppsala, Sweden) evaluation were used as the dependent variables for bulls in the training sets, whereas DRP from the December 2011 DRPs Interbull evaluation were used to compare genomic predictions with progeny test results for bulls in the testing set. Genomic predictions were more accurate than traditional pedigree indices for predicting future progeny test results of young bulls. The gain in accuracy, due to inclusion of genomic data varied by trait and ranged from 0.04 to 0.42 Pearson correlation units. Results averaged across traits showed that B-LASSO had the highest accuracy with an advantage of 0.01, 0.03 and 0.03 points in Pearson correlation compared with R-Boost, Bayes-A, and G-BLUP, respectively. The B-LASSO predictions also showed the least bias (0.02, 0.03 and 0.10 SD units less than Bayes-A, R-Boost and G-BLUP, respectively) as measured by mean difference between genomic predictions and progeny test results. The R-Boosting algorithm provided genomic predictions with regression coefficients closer to unity, which is an alternative measure of bias, for 4 out of 5 traits and also resulted in mean squared errors estimates that were 2%, 10%, and 12% smaller than B-LASSO, Bayes-A, and G-BLUP, respectively. The observed prediction accuracy obtained with these methods was within the range of values expected for a population of similar size, suggesting that the prediction method and reference population described herein are appropriate for implementation of routine genome-assisted evaluations in Spanish dairy cattle. R-Boost is a competitive marker regression methodology in terms of predictive ability that can accommodate large data sets.

Jiménez-Montero JA ，González-Recio O ，Alenda R 《-》

L2-Boosting algorithm applied to high-dimensional problems in genomic selection.

The L(2)-Boosting algorithm is one of the most promising machine-learning techniques that has appeared in recent decades. It may be applied to high-dimensional problems such as whole-genome studies, and it is relatively simple from a computational point of view. In this study, we used this algorithm in a genomic selection context to make predictions of yet to be observed outcomes. Two data sets were used: (1) productive lifetime predicted transmitting abilities from 4702 Holstein sires genotyped for 32 611 single nucleotide polymorphisms (SNPs) derived from the Illumina BovineSNP50 BeadChip, and (2) progeny averages of food conversion rate, pre-corrected by environmental and mate effects, in 394 broilers genotyped for 3481 SNPs. Each of these data sets was split into training and testing sets, the latter comprising dairy or broiler sires whose ancestors were in the training set. Two weak learners, ordinary least squares (OLS) and non-parametric (NP) regression were used for the L2-Boosting algorithm, to provide a stringent evaluation of the procedure. This algorithm was compared with BL [Bayesian LASSO (least absolute shrinkage and selection operator)] and BayesA regression. Learning tasks were carried out in the training set, whereas validation of the models was performed in the testing set. Pearson correlations between predicted and observed responses in the dairy cattle (broiler) data set were 0.65 (0.33), 0.53 (0.37), 0.66 (0.26) and 0.63 (0.27) for OLS-Boosting, NP-Boosting, BL and BayesA, respectively. The smallest bias and mean-squared errors (MSEs) were obtained with OLS-Boosting in both the dairy cattle (0.08 and 1.08, respectively) and broiler (-0.011 and 0.006) data sets, respectively. In the dairy cattle data set, the BL was more accurate (bias=0.10 and MSE=1.10) than BayesA (bias=1.26 and MSE=2.81), whereas no differences between these two methods were found in the broiler data set. L2-Boosting with a suitable learner was found to be a competitive alternative for genomic selection applications, providing high accuracy and low bias in genomic-assisted evaluations with a relatively short computational time.

González-Recio O ，Weigel KA ，Gianola D ，Naya H ，Rosa GJ ... -  《-》

Assets of imputation to ultra-high density for productive and functional traits.

The aim of this study was to evaluate different-density genotyping panels for genotype imputation and genomic prediction. Genotypes from customized Golden Gate Bovine3K BeadChip [LD3K; low-density (LD) 3,000-marker (3K); Illumina Inc., San Diego, CA] and BovineLD BeadChip [LD6K; 6,000-marker (6K); Illumina Inc.] panels were imputed to the BovineSNP50v2 BeadChip [50K; 50,000-marker; Illumina Inc.]. In addition, LD3K, LD6K, and 50K genotypes were imputed to a BovineHD BeadChip [HD; high-density 800,000-marker (800K) panel], and with predictive ability evaluated and compared subsequently. Comparisons of prediction accuracy were carried out using Random boosting and genomic BLUP. Four traits under selection in the Spanish Holstein population were used: milk yield, fat percentage (FP), somatic cell count, and days open (DO). Training sets at 50K density for imputation and prediction included 1,632 genotypes. Testing sets for imputation from LD to 50K contained 834 genotypes and testing sets for genomic evaluation included 383 bulls. The reference population genotyped at HD included 192 bulls. Imputation using BEAGLE software (http://faculty.washington.edu/browning/beagle/beagle.html) was effective for reconstruction of dense 50K and HD genotypes, even when a small reference population was used, with 98.3% of SNP correctly imputed. Random boosting outperformed genomic BLUP in terms of prediction reliability, mean squared error, and selection effectiveness of top animals in the case of FP. For other traits, however, no clear differences existed between methods. No differences were found between imputed LD and 50K genotypes, whereas evaluation of genotypes imputed to HD was on average across data set, method, and trait, 4% more accurate than 50K prediction, and showed smaller (2%) mean squared error of predictions. Similar bias in regression coefficients was found across data sets but regressions were 0.32 units closer to unity for DO when genotypes were imputed to HD density. Imputation to HD genotypes might produce higher stability in the genomic proofs of young candidates. Regarding selection effectiveness of top animals, more (2%) top bulls were classified correctly with imputed LD6K genotypes than with LD3K. When the original 50K genotypes were used, correct classification of top bulls increased by 1%, and when those genotypes were imputed to HD, 3% more top bulls were detected. Selection effectiveness could be slightly enhanced for certain traits such as FP, somatic cell count, or DO when genotypes are imputed to HD. Genetic evaluation units may consider a trait-dependent strategy in terms of method and genotype density for use in the genome-enhanced evaluations.

Jiménez-Montero JA ，Gianola D ，Weigel K ，Alenda R ，González-Recio O ... -  《-》

Accuracy of direct genomic values derived from imputed single nucleotide polymorphism genotypes in Jersey cattle.

The objective of the present study was to evaluate the predictive ability of direct genomic values for economically important dairy traits when genotypes at some single nucleotide polymorphism (SNP) loci were imputed rather than measured directly. Genotypic data consisted of 42,552 SNP genotypes for each of 1,762 Jersey sires. Phenotypic data consisted of predicted transmitting abilities (PTA) for milk yield, protein percentage, and daughter pregnancy rate from May 2006 for 1,446 sires in the training set and from April 2009 for 316 sires in the testing set. The SNP effects were estimated using the Bayesian least absolute selection and shrinkage operator (LASSO) method with data of sires in the training set, and direct genomic values (DGV) for sires in the testing set were computed by multiplying these estimates by corresponding genotype dosages for sires in the testing set. The mean correlation across traits between DGV (before progeny testing) and PTA (after progeny testing) for sires in the testing set was 70.6% when all 42,552 SNP genotypes were used. When genotypes for 93.1, 96.6, 98.3, or 99.1% of loci were masked and subsequently imputed in the testing set, mean correlations across traits between DGV and PTA were 68.5, 64.8, 54.8, or 43.5%, respectively. When genotypes were also masked and imputed for a random 50% of sires in the training set, mean correlations across traits between DGV and PTA were 65.7, 63.2, 53.9, or 49.5%, respectively. Results of this study indicate that if a suitable reference population with high-density genotypes is available, a low-density chip comprising 3,000 equally spaced SNP may provide approximately 95% of the predictive ability observed with the BovineSNP50 Beadchip (Illumina Inc., San Diego, CA) in Jersey cattle. However, if fewer than 1,500 SNP are genotyped, the accuracy of DGV may be limited by errors in the imputed genotypes of selection candidates.

Weigel KA ，de Los Campos G ，Vazquez AI ，Rosa GJ ，Gianola D ，Van Tassell CP ... -  《-》