We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and then iteratively refines estimates both on graph clustering and matrix ratings. Under a hierarchical stochastic block model that well respects practically-relevant social graphs and a low-rank rating matrix model (to be detailed), we demonstrate that our algorithm achieves the information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) that is derived by maximum likelihood estimation together with a lower-bound impossibility result. One consequence of this result is that exploiting the hierarchical structure of social graphs yields a substantial gain in sample complexity relative to the one that simply identifies different groups without resorting to the relational structure across them. We conduct extensive experiments both on synthetic and real-world datasets to corroborate our theoretical results as well as to demonstrate significant performance improvements over other matrix completion algorithms that leverage graph side information.
|Original language||English (US)|
|Journal||Advances in Neural Information Processing Systems|
|State||Published - 2020|
|Event||34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online|
Duration: Dec 6 2020 → Dec 12 2020
Bibliographical noteFunding Information:
The work of A. Elmahdy and S. Mohajer is supported in part by the National Science Foundation under Grants CCF-1617884 and CCF-1749981. The work of J. Ahn and C. Suh is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No.2018R1A1A1A05022889).
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