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

• URL: http://arxiv.org/abs/2211.09272v1
• Date: Thu, 17 Nov 2022 00:24:47 GMT
• Title: A Generalized Latent Factor Model Approach to Mixed-data Matrix Completion with Entrywise Consistency
• Authors: Yunxiao Chen, Xiaoou Li
• Abstract summary: Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. We formulate it as a low-rank matrix estimation problem under a general family of non-linear factor models. We propose entrywise consistent estimators for estimating the low-rank matrix.
• Score: 3.299672391663527
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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