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. 2019 Apr 2;79(5):931–961. doi: 10.1177/0013164419839439

Table 1.

A Small Data Set With 30 Observations and Their Values on Two Feature Variables and One Target Variable and the Summary of First Tree Iterations From XGBoost Search.

Iteration 1 (Tree 1)
 Iteration 2 (Tree 2)
 Iteration 3 (Tree 3)
RT1 RT2 y y^(0) g (1) h (1) w (1) y^(1) g (2) h (2) w (2) y^(2) g (3) h (3) w (3) y^(3) Pr
1 114 36 1 0 −0.5 0.25 −0.15 −0.15 −0.54 0.25 −0.30 −0.45 −0.61 0.24 0.31 −0.14 .46
2 92 121 1 0 −0.5 0.25 −1.04 −1.04 −0.74 0.19 −0.30 −1.34 −0.79 0.16 −0.43 −1.76 .15
3 49 24 1 0 −0.5 0.25 0.80 0.80 −0.31 0.21 −0.30 0.50 −0.38 0.23 0.31 0.81 .69
4 58 30 1 0 −0.5 0.25 −0.15 −0.15 −0.54 0.25 −0.30 −0.45 −0.61 0.24 0.31 −0.14 .46
5 40 17 1 0 −0.5 0.25 0.80 0.80 −0.31 0.21 −0.30 0.50 −0.38 0.23 0.31 0.81 .69
6 67 66 1 0 −0.5 0.25 −1.04 −1.04 −0.74 0.19 −0.30 −1.34 −0.79 0.16 0.31 −1.03 .26
7 30 79 1 0 −0.5 0.25 −1.04 −1.04 −0.74 0.19 0.47 −0.57 −0.64 0.23 0.31 −0.26 .44
8 19 14 1 0 −0.5 0.25 0.80 0.80 −0.31 0.21 0.47 1.27 −0.22 0.17 0.31 1.58 .83
9 33 8 1 0 −0.5 0.25 0.80 0.80 −0.31 0.21 0.47 1.27 −0.22 0.17 0.31 1.58 .83
10 172 38 1 0 −0.5 0.25 −0.15 −0.15 −0.54 0.25 −0.30 −0.45 −0.61 0.24 0.31 −0.14 .46
11 55 37 0 0 0.5 0.25 −0.15 −0.15 0.46 0.25 −0.30 −0.45 0.39 0.24 0.31 −0.14 .46
12 103 79 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 0.31 −1.03 .26
13 68 117 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 −0.43 −1.76 .15
14 194 17 0 0 0.5 0.25 −0.15 −0.15 0.46 0.25 −0.30 −0.45 0.39 0.24 0.31 −0.14 .46
15 68 84 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 −0.43 −1.76 .15
16 48 127 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 −0.43 −1.76 .15
17 48 200 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 −0.43 −1.76 .15
18 61 47 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 0.31 −1.03 .26
19 37 155 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 −0.43 −1.76 .15
20 58 84 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 −0.43 −1.76 .15
21 139 97 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 −0.43 −1.76 .15
22 99 84 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 −0.43 −1.76 .15
23 47 50 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 0.31 −1.03 .26
24 41 54 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 0.31 −1.03 .26
25 29 90 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 0.47 −0.57 0.36 0.23 −0.43 −0.99 .27
26 117 31 0 0 0.5 0.25 −0.15 −0.15 0.46 0.25 −0.30 −0.45 0.39 0.24 0.31 −0.14 .46
27 44 104 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 −0.43 −1.76 .15
28 34 62 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 0.31 −1.03 .26
29 83 20 0 0 0.5 0.25 −0.15 −0.15 0.46 0.25 −0.30 −0.45 0.39 0.24 0.31 −0.14 .46
30 64 57 0 0 0.5 0.25 −1.04 −1.04 0.26 0.19 −0.30 −1.34 0.21 0.16 0.31 −1.03 .26
Loss function 20.79 15.15 14.34 13.56