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Table 4:
Means and standard deviations of the third quartiles of RDEμ/rsucc for ML-estimated and fixed hyperparameter values of the DTS-CMA-ES GP models. The third quartiles are from 2×15 independent datasets per function and dimension, and the means and standard deviations are averaged across 2×23 data (24 COCO functions without Linear slopef5 in the first and second half of optimization run) for each respective dimension.
covar. fun.μ(x)2-D3-D5-D10-D20-D
KMate´rnν=5/2 ML estimate ML estimate 0.41 ±0.07 0.39 ±0.07 0.33 ±0.06 0.31 ±0.08 0.31 ±0.12 
KMate´rnν=5/2 ML estimate =1 0.41 ±0.06 0.39 ±0.07 0.38 ±0.07 0.42 ±0.06 0.45 ±0.08 
KMate´rnν=5/2 mμ=0 ML estimate 0.45 ±0.08 0.42 ±0.08 0.37 ±0.09 0.33 ±0.08 0.33 ±0.11 
KMate´rnν=5/2 mμ=0 =1 0.40 ±0.06 0.39 ±0.07 0.39 ±0.07 0.44 ±0.06 0.49 ±0.07 
KSE ML estimate ML estimate 0.41 ±0.07 0.39 ±0.07 0.35 ±0.05 0.32 ±0.08 0.37 ±0.13 
KSE ML estimate =1 0.41 ±0.06 0.40 ±0.07 0.39 ±0.07 0.42 ±0.06 0.47 ±0.09 
KSE mμ=0 ML estimate 0.45 ±0.09 0.44 ±0.09 0.39 ±0.08 0.36 ±0.10 0.58 ±0.34 
KSE mμ=0 =1 0.41 ±0.06 0.41 ±0.07 0.40 ±0.07 0.44 ±0.06 0.51 ±0.09 
covar. fun.μ(x)2-D3-D5-D10-D20-D
KMate´rnν=5/2 ML estimate ML estimate 0.41 ±0.07 0.39 ±0.07 0.33 ±0.06 0.31 ±0.08 0.31 ±0.12 
KMate´rnν=5/2 ML estimate =1 0.41 ±0.06 0.39 ±0.07 0.38 ±0.07 0.42 ±0.06 0.45 ±0.08 
KMate´rnν=5/2 mμ=0 ML estimate 0.45 ±0.08 0.42 ±0.08 0.37 ±0.09 0.33 ±0.08 0.33 ±0.11 
KMate´rnν=5/2 mμ=0 =1 0.40 ±0.06 0.39 ±0.07 0.39 ±0.07 0.44 ±0.06 0.49 ±0.07 
KSE ML estimate ML estimate 0.41 ±0.07 0.39 ±0.07 0.35 ±0.05 0.32 ±0.08 0.37 ±0.13 
KSE ML estimate =1 0.41 ±0.06 0.40 ±0.07 0.39 ±0.07 0.42 ±0.06 0.47 ±0.09 
KSE mμ=0 ML estimate 0.45 ±0.09 0.44 ±0.09 0.39 ±0.08 0.36 ±0.10 0.58 ±0.34 
KSE mμ=0 =1 0.41 ±0.06 0.41 ±0.07 0.40 ±0.07 0.44 ±0.06 0.51 ±0.09 
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