Algorithm 3: ADTree with Adaboost

Input: Training Dataset -D

1. Process of Initialization

1.a Set $w_{i,t}$ = 0 = 1/n $\forall i and P_{t=1}$ = {true}

1.b First DT rule $r_0$(x): { if (true) then $[if \left(true\right){\alpha }_0$ = $\frac{1}{2}$ ln ($\frac{W+\left(true\right)}{W-\left(true\right)}) else 0]$ else 0}

1.c Update $w_{i,t}$ = 1 = $w_{i,t}$ = 0 exp$(-r_0$ $\left(x^{\left(i\right)}\right) y^{\left(i\right)})$

2. Do it again for boosting cycle t = 1:T

2.1 For every pre-condition $C_1\in P_t$ and each condition $C_2\in C, evaluate$

Z$(c_1, c_2)=2(\sqrt{W+\left(c_1{\displaystyle \cap }{c}_2\right)W-\left(c_1{\displaystyle \cap }{c}_2\right)}$ + $\sqrt{W+\left(c_1{\displaystyle \cap }\neg c_2\right)W-\left(c_1{\displaystyle \cap }\neg c_2\right)}$+ W($\neg c_2)$

2.1 Compute ${\alpha }_t^{+}$ and ${\alpha }_t^{-}$ for the selected $c_1^{\ast } and {\alpha }_1^{\ast }$ that minimizes Z with $\delta$ = 1

${\alpha }_t^{+}$ = $\frac{1}{2}$ ln ($\frac{W+\left(c_1^{\ast } {\displaystyle \cap } c_2^{\ast } \right)+\delta }{W-\left(c_1^{\ast } {\displaystyle \cap } c_2^{\ast } \right)+\delta }$), ${\alpha }_t^{-}$ = $\frac{1}{2}$ =l n($\frac{W+(c_1^{\ast } {\displaystyle \cap }\neg c_2^{\ast } )+\delta }{W-(c_1^{\ast } {\displaystyle \cap }\neg c_2^{\ast } )+\delta }$)

2.2 Update $P_{t+1}$: $P_t {\displaystyle \cup }$ { $c_1^{\ast } {\displaystyle \cap } c_2^{\ast }$, $c_1^{\ast } {\displaystyle \cap }\neg c_2^{\ast }\}$

2.3 Update $W_{i,t+1}$ = $W_{i,t}$ exp(- $r_t$ ($x^{\left(i\right)}) y^{\left(i\right)})$

Output: F(x) = ${{\displaystyle \sum }}_{t=1}^T{r}_1\left(x\right)$