Genome-wide prediction using Bayesian additive regression trees

Table 2 Mean squared prediction error (MSPE) for the LASSO, Bayesian LASSO (BLASSO), genomic BLUP (GBLUP), reproducing kernel Hilbert space (RKHS) regression, random forests (RF) and Bayesian additive regression trees (BART) methods evaluated on the simulated QTLMAS2010 data when dominance and epistatic effects were added

Method	Mean squared prediction error (MSPE)
LASSO
minMSE	83.377
minMSE + 1SE	84.832
BLASSO	71.857
GBLUP	92.296
RKHS
\(h = 0.05\)	92.361
\(h = 0.1\)	91.852
\(h = 0.25\)	91.906
RF	M = 10	M = 25	M = 50	M = 100	M = 200	M = 400	M = 600
	107.908	105.123	100.784	101.992	100.327	100.900	99.836
BART	M = 10	M = 25	M = 50	M = 100	M = 200	M = 400	M = 600
\(q = 0.9\)
\(\kappa\) = 2	80.717	76.892	70.845	65.294	65.196	66.283	66.906
\(\kappa\) = 3	79.277	72.720	67.061	65.120	64.943	65.542	66.593
\(\kappa\) = 4	87.030	71.401	65.635	64.353	65.149	66.483	68.050
\(\kappa\) = 5	79.249	71.243	67.748	64.741	65.611	68.290	70.510
\(q = 0.95\)
\(\kappa\) = 2	86.328	70.452	67.744	65.465	65.308	65.801	66.998
\(\kappa\) = 3	76.438	69.833	67.123	65.522	65.045	65.513	66.601
\(\kappa\) = 4	86.653	74.651	67.164	67.220	65.074	66.544	68.163
\(\kappa\) = 5	90.456	69.571	65.085	66.086	65.790	68.298	70.566

The lowest MSPE obtained with each method is highlighted in italics. h is the bandwidth of the radial basis function kernel. M is the number of trees for RF and BART, and \(q\) and \(\kappa\) are hyperparameters of the BART priors. The stopping criteria for the regularization coefficient λ in LASSO were obtained based on tenfold cross-validation both at minimum MSE and minimum MSE plus 1 standard error [42]

ISSN: 1297-9686