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.

翻译：矩阵完成是一个机器学习方法的类别,涉及对部分观察的矩阵中缺失条目的预测。本文研究混合数据的完成情况,即涉及多种变量(如连续、二进制、正态)的数据。我们在非线性因素模型的一般组合下将它作为一个低级别矩阵估计问题来拟订,然后为估计低级矩阵提出入门一致的估算标准。为拟议的估算者得出了粗略的概率错误界限。提议的方法通过模拟研究和用于合作过滤和大规模教育评估的实际数据应用加以评价。