Algorithm 3 Tensor LogitBoost

$$\begin{array}{cc}\hfill & \text{Initialize:}F({\mathit{X}}_i)=0\text{and}p({\mathit{X}}_i)=1∕2,i=1,\dots ,n\hfill \\ \hfill & \mathbf{for}l=1,\dots ,L\mathbf{do}\hfill \\ \hfill & \text{Compute responses and weights}\hfill \\ \hfill & z_i=\frac{y_i-p({\mathit{X}}_i)}{p({\mathit{X}}_i)[1-p({\mathit{X}}_i)]},\hfill \\ \hfill & w_i=p({\mathit{X}}_i)[1-p({\mathit{X}}_i)];\hfill \\ \hfill & \text{Fit a weighted tensor linear regression with responses}\hfill \\ \hfill & z_i,\text{predictors}{\mathit{X}}_i\text{with weights}{w}_i;\hfill \\ \hfill & \text{Denote the fitted values by}{\widehat{f}}_l;\hfill \\ \hfill & \text{Update the regression function by the fitted values}\hfill \\ \hfill & F\leftarrow F+{\widehat{f}}_l,\hfill \\ \hfill & p\leftarrow \frac{1}{1+e^{-F}};\hfill \\ \hfill & \mathbf{end}\mathbf{for}\hfill \\ \hfill & \text{Output the classifier}F(\mathit{X})=\text{sgn}[\sum \begin{array}{c}L\hfill \\ l=1\hfill \end{array}{\widehat{f}}_l(\mathit{X})].\hfill \end{array}$$