# Structured Matrix Completion with Applications to Genomic Data Integration

arXiv: https://arxiv.org/abs/1504.01823 · HTML: https://mlsanity.com/paper/1504.01823/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2015.

## Built on by (most cited first, 17 of 17)

- [A Variational Information Bottleneck Approach to Multi-Omics Data Integration](https://mlsanity.com/paper/2102.03014/) (2021)
- [Provable Tensor-Train Format Tensor Completion by Riemannian Optimization](https://mlsanity.com/paper/2108.12163/) (2021)
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- [Multi-source Learning via Completion of Block-wise Overlapping Noisy Matrices](https://mlsanity.com/paper/2105.10360/) (2021)
- [Representation Retrieval Learning for Heterogeneous Data Integration](https://mlsanity.com/paper/2503.09494/) (2025)
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- [A Locally Adaptive Algorithm for Multiple Testing with Network Structure](https://mlsanity.com/paper/2203.11461/) (2022)
- [Prediction approaches for partly missing multi-omics covariate data: A literature review and an empirical comparison study](https://mlsanity.com/paper/2302.03991/) (2023)
- [CLCLSA: Cross-omics Linked embedding with Contrastive Learning and Self Attention for multi-omics integration with incomplete multi-omics data](https://mlsanity.com/paper/2304.05542/) (2023)
- [Using Interpretable Machine Learning to Massively Increase the Number of Antibody-Virus Interactions Across Studies](https://mlsanity.com/paper/2206.14566/) (2022)
- [Imputation of missing values in multi-view data](https://mlsanity.com/paper/2210.14484/) (2022)
- [Nonparametric Trace Regression in High Dimensions via Sign Series Representation](https://mlsanity.com/paper/2105.01783/) (2021)
- [Statistical Inference for High-Dimensional Linear Regression with Blockwise Missing Data](https://mlsanity.com/paper/2106.03344/) (2021)
- [Empirical Bayes Linked Matrix Decomposition](https://mlsanity.com/paper/2408.00237/) (2024)
- [Fast and Provable Tensor-Train Format Tensor Completion via Precondtioned Riemannian Gradient Descent](https://mlsanity.com/paper/2501.13385/) (2025)
- [Statistical Matching via Schr"odinger Bridge beyond Conditional Independence](https://mlsanity.com/paper/2606.22770/) (2026)

## Abstract (arXiv)

Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.