A Generalized Latent Factor Model Approach to Mixed-data Matrix Completion with Entrywise Consistency
This addresses the problem of handling diverse data types in matrix completion for practitioners in fields like recommendation systems and education, though it appears incremental as it extends existing factor models to mixed data.
The paper tackles matrix completion for mixed data types by formulating it as a low-rank estimation problem under non-linear factor models and proposing entrywise consistent estimators, with tight error bounds and validation through simulations and real-world applications like collaborative filtering and educational assessment.
Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables (e.g., continuous, binary, ordinal). We formulate it as a low-rank matrix estimation problem under a general family of non-linear factor models and then propose entrywise consistent estimators for estimating the low-rank matrix. Tight probabilistic error bounds are derived for the proposed estimators. The proposed methods are evaluated by simulation studies and real-data applications for collaborative filtering and large-scale educational assessment.