Active Learning Algorithms for Graphical Model Selection: Supplementary Material

Proof. To prove this theorem, we will use a simple argument that can be thought of as a proof by probabilistic induction. Towards this end, we will let Ek be the event that Algorithm 1 succeeds at iteration number k. Notice that k takes values in the set {1, 2, . . . , blog2(2p)c} since the algorithm terminates when the (doubling) counter satisfies ` = 2k−1 ≥ 2p. We can characterize the event Ek as follows: