A Masked Mixture Model for Compact and Accurate Matrix Factorization

Matrix factorization (MF) is a widely used backbone for modeling large relational data due to its simplicity, scalability, and interpretability. However, classical MF uses a single shared latent basis, which can be overly restrictive for heterogeneous matrices. In this paper, we propose Masked Mixture Factorization (MMF), a lightweight yet effective MF variant that adapts to heterogeneous interactions through instance-wise latent gating, substantially improving accuracy under the same parameter budget while retaining MF's scalability. We provide theoretical results on MMF's expressivity and identifiability, clarifying when masking expands representational power and when the model is recoverable. Extensive experiments on matrix reconstruction, matrix completion, and Top-N recommendation show consistent gains over strong baselines.