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

arXiv: https://arxiv.org/abs/2211.09272 · HTML: https://mlsanity.com/paper/2211.09272/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 17 Nov 2022.

## Builds on (most cited first, 15 of 15)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization](https://mlsanity.com/paper/1902.07698/) (2019)
- [Inference and Uncertainty Quantification for Noisy Matrix Completion](https://mlsanity.com/paper/1906.04159/) (2019)
- [A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion](https://mlsanity.com/paper/1309.6013/) (2013)
- [Matrix Completion via Max-Norm Constrained Optimization](https://mlsanity.com/paper/1303.0341/) (2013)
- [Statistical Inferences of Linear Forms for Noisy Matrix Completion](https://mlsanity.com/paper/1909.00116/) (2019)
- [Adaptive Multinomial Matrix Completion](https://mlsanity.com/paper/1408.6218/) (2014)
- [Poisson Matrix Recovery and Completion](https://mlsanity.com/paper/1504.05229/) (2015)
- [Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications](https://mlsanity.com/paper/1712.08966/) (2017)
- [A General Pairwise Comparison Model for Extremely Sparse Networks](https://mlsanity.com/paper/2002.08853/) (2020)
- [A Note on Exploratory Item Factor Analysis by Singular Value Decomposition](https://mlsanity.com/paper/1907.08713/) (2019)
- [Inference for Low-Rank Models](https://mlsanity.com/paper/2107.02602/) (2021)
- [Network Topology Mapping from Partial Virtual Coordinates and Graph Geodesics](https://mlsanity.com/paper/1809.03319/) (2018)
- [Determining the Number of Factors in High-dimensional Generalized Latent Factor Models](https://mlsanity.com/paper/2010.02326/) (2020)
- [Main effects and interactions in mixed and incomplete data frames](https://mlsanity.com/paper/1806.09734/) (2018)

## Built on by (most cited first, 1 of 1)

- [Generalized Grade-of-Membership Estimation for High-dimensional Locally Dependent Data](https://mlsanity.com/paper/2412.19796/) (2024)

## Abstract (arXiv)

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.