A Generalized Latent Factor Model Approach to Mixed-data Matrix Completion with Entrywise Consistency

TL;DR

This paper introduces a unified low-rank matrix estimation framework for mixed data types, providing entrywise consistent estimators with theoretical error bounds, validated through simulations and real-world applications.

Contribution

It develops a generalized latent factor model approach for mixed-data matrix completion, offering novel estimators with proven consistency and error bounds.

Findings

Estimators achieve entrywise consistency under broad conditions.

Theoretical error bounds are derived for the proposed estimators.

Methods perform well in collaborative filtering and educational assessment tasks.

Abstract

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.