# On the Fundamental Limits of Matrix Completion: Leveraging Hierarchical Similarity Graphs

@article{Ahn2021OnTF, title={On the Fundamental Limits of Matrix Completion: Leveraging Hierarchical Similarity Graphs}, author={Junhyung Ahn and Adel M. Elmahdy and Soheil Mohajer and Changho Suh}, journal={ArXiv}, year={2021}, volume={abs/2109.05408} }

We study the matrix completion problem that leverages hierarchical similarity graphs as side information in the context of recommender systems. Under a hierarchical stochastic block model that well respects practically-relevant social graphs and a low-rank rating matrix model, we characterize the exact information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) by proving sharp upper and lower bounds on the sample complexity. In the achievability proof…

## One Citation

Matrix Completion with Hierarchical Graph Side Information

- Computer Science, MathematicsNeurIPS
- 2020

This work develops a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and then iteratively refines estimates both on graph clusters and matrix ratings that achieves the information-theoretic limit on the number of observed matrix entries.

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