统计学习精要 (Elements of Statistical Learning ) 习题 5.9

统计学习精要 (Elements of Statistical Learning ) 习题 5.9

Derive the Reinsch form $S_{\lambda} = (1 + \lambda K)^{-1}$ for the smoothing spline.

思路：

按照课本154页的（5.18）, $\min_f (y-f)^T(y-f) + \lambda f^T K f$, 其解是 $\hat{f} = (I + \lambda K)^{-1}$。 替换 $f = N \theta$，罚项变为$\theta^T \Omega_N \theta$，则变为（5.11），解为（5.14）的f̂