Inductive Relational Matrix Completion

Data sparsity and cold-start issues emerge as two major bottlenecks for matrix completion in the context of user-item interaction matrix. We propose a novel method that can fundamentally address these issues. The main idea is to partition users into support users, which have many observed interactions (i.e., non-zero entries in the matrix), and query users, which have few observed entries. For support users, we learn their transductive preference embeddings using matrix factorization over their interactions (a relatively dense sub-matrix). For query users, we devise an inductive relational model that learns to estimate the underlying relations between the two groups of users. This allows us to attentively aggregate the preference embeddings of support users in order to compute inductive embeddings for query users. This new method can address the data sparsity issue by generalizing the behavior patterns of warm-start users to others and thus enables the model to also work effectively for cold-start users with no historical interaction. As theoretical insights, we show that a general version of our model does not sacrifice any expressive power on query users compared with transductive matrix factorization under mild conditions. Also, the generalization error on query users is bounded by the numbers of support users and query users' observed interactions. Moreover, extensive experiments on real-world datasets demonstrate that our model outperforms several state-of-the-art methods by achieving significant improvements on MAE and AUC for warm-start, few-shot (sparsity) and zero-shot (cold-start) recommendation.