Statistical Learning with Sparsity

266 GRAPHS AND MODEL SELECTION

(b) Show how to use the solution θ

12

to update the current version of W and

b

Θ in O(p

2

) operations.

(c) Likewise, show how to move to a new block of equations in O(p

2

) opera-

tions.

(d) You have derived a primal graphical lasso algorithm. Write it down in

algorithmic form, as in Algorithm 9.1

(Mazumder and Hastie 2012)

Ex. 9.8 Derive the conditional distributions (9.29) and (9.30) for the mixed

graphical model.

Ex. 9.9 Close inspection of the pairwise Markov random field model (9.28)

will show that it is overparametrized with respect to the discrete potentials

ρ

sj

and ψ

jr

. This exercise shows that this aliasing is resolved by ...