Algorithm 3 Serial implementation of eXtreme Gradient Boosting

Input: $\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}\_\mathit{d}\mathit{a}\mathit{t}\mathit{a}$ → Features, thresholds, left and right             children’s nodes 1: Step 1: Development of the $\mathit{t}\mathit{r}\mathit{e}\mathit{e}\_\mathit{s}\mathit{t}\mathit{r}\mathit{u}\mathit{c}\mathit{t}\mathit{u}\mathit{r}\mathit{e} function$ 2: The single tree outputs the probability value of its class 3: Step 2: Building of the forest 4: $\mathbf{f}\mathbf{o}\mathbf{r} i=0 to {\mathit{n}}_{\mathit{c}\mathit{l}\mathit{a}\mathit{s}\mathit{s}}-1$ 5:  $\mathbf{f}\mathbf{o}\mathbf{r} e=0 to {\mathit{n}}_{\mathit{t}\mathit{r}\mathit{e}\mathit{e}\mathit{s}}-1$ 6:     ${\mathit{Z}}_{\mathit{i}}+=\mathit{t}\mathit{r}\mathit{e}\mathit{e}\_\mathit{s}\mathit{t}\mathit{r}\mathit{u}\mathit{c}\mathit{u}\mathit{t}\mathit{r}\mathit{e}(\mathit{i}\mathit{n}\mathit{p}\mathit{u}\mathit{t}\_\mathit{d}\mathit{a}\mathit{t}\mathit{a}, e\ast {\mathit{n}}_{\mathit{c}\mathit{l}\mathit{a}\mathit{s}\mathit{s}}+i)$; 7:  $\mathbf{e}\mathbf{n}\mathbf{d}$ 8: $\mathbf{e}\mathbf{n}\mathbf{d}$ 9: $Step 3:Final probability array through soft-\mathit{max}function$ 10: $\mathbf{f}\mathbf{o}\mathbf{r} i=0 to {\mathit{n}}_{\mathit{c}\mathit{l}\mathit{a}\mathit{s}\mathit{s}}-1$ 11:    ${\mathit{Z}\mathit{E}}_{\mathit{i}}=\exp \left({\mathit{Z}}_{\mathit{i}}\right);$ 12: end 13: $\mathbf{f}\mathbf{o}\mathbf{r} i=0 to {\mathit{n}}_{\mathit{c}\mathit{l}\mathit{a}\mathit{s}\mathit{s}}-1$ 14:    $\mathit{z}=\sum _{i€{\mathit{n}}_{\mathit{c}\mathit{l}\mathit{a}\mathit{s}\mathit{s}}}{\mathit{Z}\mathit{E}}_{\mathit{i}};$ 15: end 16: $\mathbf{f}\mathbf{o}\mathbf{r} i=0 to {\mathit{n}}_{\mathit{c}\mathit{l}\mathit{a}\mathit{s}\mathit{s}}-1$ 17:    ${\mathit{P}}_{\mathit{i}}={\mathit{Z}\mathit{E}}_{\mathit{i}}/\mathit{z};$ 18: end 19: $\mathrm{F}\mathrm{i}\mathrm{n}\mathrm{d} \mathit{i}\mathit{m}\mathit{a}\mathit{x}, \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x} \mathrm{o}\mathrm{f} \mathrm{t}\mathrm{h}\mathrm{e} {\mathit{P}}_{\mathit{i}} \mathrm{m}\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{m}\mathrm{u}\mathrm{m}$ Output: $\mathit{i}\mathit{m}\mathit{a}\mathit{x}$