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In the second stage, these residuals were regressed on ROH4Mb using a single marker regression model and a gradient boosted machine (GBM) algorithm.
The ROH4Mb effect of a SNP was estimated by regressing ROH4Mb of a SNP on the same phenotype as single marker regression and gradient boosted machine and therefore the additive effect explained by the EBV was removed from the phenotype.
The second stage involved using the residuals from the first stage as a phenotype and regress these on the ROH4Mb status utilizing a single marker regression and gradient boosted machine (GBM).
The approach is based on Random Forest and Gradient Boosted Machine algorithms.
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Generalized boosted regression is an implementation of expansion to Freund and Schapire's AdaBoost algorithm and J. Friedman's gradient boosting machine (Freund and Schapire 1997).
From pairs with observed binding affinities, it trains a gradient boosting machine model to learn the nonlinear relationships between the features and the binding affinities.
The regression algorithms applied to this end were: partial least square regression (PLS), gradient boosting machine (GBM) and support vector machine (SVM).
Six ML algorithms, including logistic regression, decision tree, random forest, gradient boosting machine, support vector machine, and multilayer perceptron neural network, were used for the relationship modelling and firefly algorithm (FA) was used for the hyper-parameters tuning.
We choose the gradient boosting machine as our model, which was originally proposed in [37], because of its following benefits [38, 39]: Accuracy: the boosting algorithm is an ensemble model, which trains a sequence of "weak learners" to gradually achieve a good accuracy.
The existence of gene-gene interactions was first explored by a data mining technique similar to the Adaboost algorithm, and based on classification and regression trees (CART): the gradient boosting machine [44].
All results reported here were obtained using the gbm package in R [44] which implements extensions to Friedman's gradient boosting machine [45], [46], [47], and has the additional advantages of handling missing data and of allowing weighting of data.
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