Given $\{\mathbf{x}_i,y_i\}, i=1,\ldots,m$, consider the following optimization problem:
$\min\limits_{\mathbf{w},b} \sum\limits_{i=1}^{m}\log(1+\exp(-y_i(\mathbf{w^Tx_i} + b)))$ $+\lambda|| \mathbf{w}||^2_2$
Solving the above optimization problem will give me a linear classifier. However, I want to use a kernel to get a non linear classifier. Using Representer theorem, the above regularized ERM is written as follows :
$\min\limits_{\alpha_j, j=1,\cdots,m} \sum\limits_{i=1}^{m}\log(1+\exp(-\sum\limits_{j=1}^{m}y_i\alpha_jK(\mathbf{x}_i,\mathbf{x}_j)))$ $+\lambda\sum\limits_{i=1}^{m}\sum\limits_{j=1}^{m}\alpha_i\alpha_jK(\mathbf{x}_i,\mathbf{x}_j)$
where $K(\cdot,\cdot)$ is the kernel function.
I was trying to reproduce Table 2 (1st column) results from a research paper using above idea. However, I am not getting the results presented using the parameters given.
Is there something which I am missing on? Any references are also welcomed.
