# Mixed Matrix Completion in Complex Survey Sampling under Heterogeneous Missingness

arXiv: https://arxiv.org/abs/2402.03954 · HTML: https://mlsanity.com/paper/2402.03954/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Builds on (most cited first, 8 of 8)

- [Generalized Low Rank Models](https://mlsanity.com/paper/1410.0342/) (2014)
- [Provable Inductive Matrix Completion](https://mlsanity.com/paper/1306.0626/) (2013)
- [Generalized High-Dimensional Trace Regression via Nuclear Norm Regularization](https://mlsanity.com/paper/1710.08083/) (2017)
- [Collective Matrix Completion](https://mlsanity.com/paper/1807.09010/) (2018)
- [Max-Norm Optimization for Robust Matrix Recovery](https://mlsanity.com/paper/1609.07664/) (2016)
- [Main effects and interactions in mixed and incomplete data frames](https://mlsanity.com/paper/1806.09734/) (2018)
- [Matrix Completion under Low-Rank Missing Mechanism](https://mlsanity.com/paper/1812.07813/) (2018)
- [Transductive Matrix Completion with Calibration for Multi-Task Learning](https://mlsanity.com/paper/2302.09834/) (2023)

## Built on by (most cited first, 2 of 2)

- [Causal Customer Churn Analysis with Low-rank Tensor Block Hazard Model](https://mlsanity.com/paper/2405.11377/) (2024)
- [Computational Efficient and Minimax Optimal Nonignorable Matrix Completion](https://mlsanity.com/paper/2504.04016/) (2025)

## Abstract (arXiv)

Modern surveys with large sample sizes and growing mixed-type questionnaires require robust and scalable analysis methods. In this work, we consider recovering a mixed dataframe matrix, obtained by complex survey sampling, with entries following different canonical exponential distributions and subject to heterogeneous missingness. To tackle this challenging task, we propose a two-stage procedure: in the first stage, we model the entry-wise missing mechanism by logistic regression, and in the second stage, we complete the target parameter matrix by maximizing a weighted log-likelihood with a low-rank constraint. We propose a fast and scalable estimation algorithm that achieves sublinear convergence, and the upper bound for the estimation error of the proposed method is rigorously derived. Experimental results support our theoretical claims, and the proposed estimator shows its merits compared to other existing methods. The proposed method is applied to analyze the National Health and Nutrition Examination Survey data.