I am studying Machine Learning Probability perspective and I have a question with Algorithm 8.2, which is
$\mathbf{w} = 0_{D}$ $w_{0} = \log (\bar{y}/(1-\bar{y}))$
Repeat:
$\eta_{i} = w_{0}+\mathbf{w}^{T} \mathbf{x}_{i}$
$\mu_{i} = \text{sigm}(\eta_{i})$
$s_{i} = \mu_{i}(1-\mu_{i})$
$z_{i} = \eta_{i}+\frac{y_{i}-\mu_{i}}{s_{i}}$
$\mathbf{S} = \text{diag}(s_{1:N})$
$\mathbf{w} = (\mathbf{X}^{T}\mathbf{S}\mathbf{X})^{-1}\mathbf{X}^{T}\mathbf{S}\mathbf{z}$
until converged
I think $w_{0}$ means the coefficient of intercept, but why it is not updated in the loop?
It seems like $w_{0}$ is fixed like a constant?