Exercise 7.3 - Centering and ridge regression

Answers

The loss is given by:

L (𝐰, w_{0}) = {(𝐲 - 𝐗^{T} 𝐰 - w_{0} 1)}^{T} (𝐲 - 𝐗^{T} 𝐰 - w_{0} 1) .

Taking partial gradient w.r.t. $w_{0}$ yields:

\frac{\partial}{\partial w_{0}} L = \frac{1^{T} (𝐲 - 𝐗^{T} 𝐰)}{N} .

Setting it to zero gives (7.94), where we have made use of $\bar{x} = 0$ .

Taking partial gradient w.r.t. $𝐰$ yields:

𝐰^{MLE} = {(𝐗 𝐗^{T} + λ 𝐈)}^{- 1} 𝐗 (𝐲 - w_{0} 1) .

In the equation (7.95), the observed data has to be centralized.

solour_lfq

2021-03-24 13:42