Exercise 13.10 - GSM representation of group lasso

Note that the prior over ${\mathbf{\text{𝐰}}}_g$ takes the form:

Therefore its logarithm takes the form:

where $c$ is a term that is independent from ${\mathbf{\text{𝐰}}}_g$ and the data. Combining this term with the ordinary data-dependent NLL yields the loss function of the group lasso.