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.