Ex. 12.3

Ex. 12.3

Consider a modification to (12.43) where you do not penalize the constant. Formulate the problem, and characterize its solution.

Soln. 12.3

This exercise is closely related to Section 5.8.1 and 12.3.3. Specifically, without the constant term \(\beta_0\), (12.43) can be rewritten as

\[\begin{equation} \label{ex:12-3a} \min_{\bm{\beta}}V(\by, \bb{K}\bm{\beta}) + \frac{\lambda}{2}\|\bm{\beta}\|^2, \end{equation}\]

where \(\bb{K}_{ij} = K(x_i, x_j)\) as usual. For general error measure \(V\), the optimization problem \(\eqref{ex:12-3a}\) can be solved numerically.