Algorithm 3 ADT training process

1:Define a prior-tree, $T_0$   2:Train $T_0$ with $x_{\mathrm{train}}(X,V_M)$ and $y_{\mathrm{train}}\left(X\right)$   3:$V_0^o\leftarrow V_M$   4:$K\leftarrow 1$   5:$E_0\leftarrow L_0$   6:for $m=1,2,\dots ,M$ do   7:      $K^{\prime }\leftarrow K$   8:      for $k=0,1,\dots ,K-1$ do   9:            $k^{\prime }\leftarrow K-1$ 10:            for $n\in E_k$ do 11:                   $k^{\prime }\leftarrow k^{\prime }+1$ 12:                   Define a prospective tree $T^{\prime }$ 13:                   Train $T^{\prime }$ with $x_{\mathrm{train}}(X_{k,n},V\setminus V_k^o)$ and $y_{\mathrm{train}}\left(X_{k,n}\right)$ 14:                   Select $j_{\mathrm{sel},k^{\prime }}$, of which feature has highest feature importance in $T^{\prime }$ 15:                   $V_{k^{\prime }}^o\leftarrow V_k^o\cup \left\{j_{\mathrm{sel},k^{\prime }}\right\}$ 16:                   Discard $T^{\prime }$ 17:                   Define a new sub tree $T_{k^{\prime }}$ 18:                   $X_{k^{\prime }}\leftarrow X_{k,n}$ 19:                   Train $T_{k^{\prime }}$ with $x_{\mathrm{train}}(X_{k^{\prime }},V_{k^{\prime }}^o)$ and $y_{\mathrm{train}}\left(X_{k^{\prime }}\right)$ 20:                   Prune $T_{k^{\prime }}$ at depth of best accuracy on $x_{\mathrm{val}}(X_{k^{\prime }},V_{k^{\prime }}^o)$ and $y_{\mathrm{val}}\left(X_{k^{\prime }}\right)$ 21:                   $T_{k,n}\leftarrow T_{k^{\prime },0}$ (Graft $T_k^{\prime }$ to the leaf of $T_k$) 22:                   $E_{k^{\prime }}\leftarrow L_{k^{\prime }}$ 23:                   $E_k\leftarrow E_k-\left\{n\right\}$ 24:                   $K^{\prime }\leftarrow K^{\prime }+1$ 25:            end for 26:      end for 27:      $K\leftarrow K^{\prime }$ 28:end for