APr o of s A.1 Proof of theorem 1 W œS

B . 15 E -Prior In this case the prior reads: P A.3 Proof of theorem 2 We consider the following hierarchical model, for The above problem is non-convex because of the rank constraint (17). We focus on finding the optimal eigenvectors first. Note that this solution is not unique if there are repeated eigenvalues. A.4 Proof of Corollary 1 With the presented hierarchical model (Figure 1), the coupling problem is the following: min Note that the solution does not depend on Á . Figure 3: Graphical representation of the hierarchical model considered in section 4.2.