Discrete-valued Preference Estimation with Graph Side Information

Incorporating graph side information into recommender systems has been widely used to better predict ratings, but relatively few works have focused on theoretical guarantees. Ahn et al. (2018) firstly characterized the optimal sample complexity in the presence of graph side information, but the results are limited due to strict, unrealistic assumptions made on the unknown preference matrix. In this work, we propose a new model in which the unknown preference matrix can have any discrete values, thereby relaxing the assumptions made in prior work. Under this new model, we fully characterize the optimal sample complexity and develop a computationally-efficient algorithm that matches the optimal sample complexity. We also show that our algorithm is robust to model errors, and it outperforms existing algorithms on both synthetic and real datasets.