Q1 [partially_resolved] General problem (Sec. 1-2, 4): given a hypothesis space H of factored preferential attachment functions f(l,G,A)=f_l(l) f_d(|A|) prod_{v in A} f_v(l,G,v)/Z on vertex-labeled graphs, a loss L, an integer t and a single snapshot G^(t) generated by unknown f* in H, find f-hat minimizing L(f*,f-hat); a 'learning bound' is an algorithm A and polynomial p with P(L(f*,A(G^(t)))<eps)>1-delta whenever t>=p | remains open: Prove (or refute) a finite-sample learning bound - an explicit algorithm and polynomial p(1/eps,1/delta) with P(L(f*,A(G^(t)))<eps)>1-delta - for any nontrivial hypothesis class of factored, label-dependent preferential attachment functions (|Sigma|>1, m>=1 edges per new vertex, general f_l,f_d,f_v)
Q2 [open] Labeled Barabasi-Albert model (Sec. 3, second example): vertices receive label 1 w.p. p and 0 w.p. 1-p, each new vertex attaches to exactly m existing vertices with f_v(l,G,v) = |N_G^0(v)| + w |N_G^1(v)| (weighted degree, label-1 neighbours weighted by w>0). The paper shows the asymptotic edge-endpoint-pair distribution ((1-p)^2, p^2, 2p(1-p)) and the label distribution do not depend on w, so 'the