L2 regularization

$$\frac {1} {N} \sum_{n=1}^N \log (1+\exp(-y_n W^T X_n)) + \lambda \left \| W \right \|_2^2$$

kernel logistic regression###

带L2正则的LR：

$$\min_W \frac {\lambda} {N} W^TW + \frac {1} {N} \sum_{n=1}^N \log (1+\exp(-y_n W^T X_n)) \\ W = \sum_{n=1}^N \beta_n X_n \\ \min_{\beta} \frac {\lambda} {N} \sum_{n=1}^N \sum_{m=1}^n \beta_n \beta_m K(X_n,X_m) + \frac {1} {N} \sum_{n=1}^N \log (1+\exp(-y_n \sum_{m=1}^N \beta_m K(X_m,X_n) ))$$

为什么W的最优解是X的线性组合？

求解###

坐标下降法等