Web Appendix of “A Group-Specific Recommender System” Xuan Bi, Annie Qu, Junhui Wang and Xiaotong Shen ∗ Proof of Lemma 1 By Theorem 2.1 of Ansley and Kohn (1994), each of (3) and (4) has a unique solution, and the back-fitting algorithms for (5) and (6) can be applied in (3), and (7) and (8) can be applied in (4). This guarantees convergence to the unique solution given any initial value. Therefore, Algorithm 1 is equivalent to minimizing (3) and (4) iteratively. Note that minimizing (3) and (4) iteratively is a special case of Algorithm MBI (Chen et al., 2012) with two blocks. Therefore, following Theorem 3.1 of Chen et al. (2012), Algorithm 1 converges to a stationary point. This completes the proof. Proof of Lemma 2 Since θ ui =(p u + s vu ) ′ (q i + t j i ) is a quadratic function of (p ′ u , q ′ i , s ′ vu , t ′ j i ) ′ , and given that ‖(p ′ u , q ′ i , s ′ vu , t ′ j i ) ′ ‖ ∞ and ‖(˜ p ′ u , ˜ q ′ i , ˜ s ′ vu , ˜ t ′ j i ) ′ ‖ ∞ are bounded by L, there exists a constant C 1 ≥ * Xuan Bi is Ph.D. student, Department of Statistics, University of Illinois at Urbana-Champaign, Cham- paign, IL 61820 (E-mail: xuanbi2@illinois.edu). Annie Qu is Changjiang Visiting Professor, Yunnan Univer- sity, China, and Professor, Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL 61820 (E-mail: anniequ@illinois.edu). Junhui Wang is Associate Professor, Department of Mathematics, City University of Hong Kong, Hong Kong, China (E-mail: junhwang@cityu.edu.hk). Xiaotong Shen is Professor, School of Statistics, University of Minnesota, Minneapolis, MN 55455 (E-mail: xshen@umn.edu). 1