# Multi-source Learning via Completion of Block-wise Overlapping Noisy Matrices

arXiv: https://arxiv.org/abs/2105.10360 · HTML: https://mlsanity.com/paper/2105.10360/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 108 references that are in the map.
- First posted on arXiv 21 May 2021.

## Builds on (most cited first, 30 of 30)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [KG-BERT: BERT for Knowledge Graph Completion](https://mlsanity.com/paper/1909.03193/) (2019)
- [Scalable and accurate deep learning for electronic health records](https://mlsanity.com/paper/1801.07860/) (2018)
- [Exploiting Similarities among Languages for Machine Translation](https://mlsanity.com/paper/1309.4168/) (2013)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis](https://mlsanity.com/paper/1704.00708/) (2017)
- [Matrix Completion has No Spurious Local Minimum](https://mlsanity.com/paper/1605.07272/) (2016)
- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Offline bilingual word vectors, orthogonal transformations and the inverted softmax](https://mlsanity.com/paper/1702.03859/) (2017)
- [Guaranteed Matrix Completion via Non-convex Factorization](https://mlsanity.com/paper/1411.8003/) (2014)
- [Gradient Descent Can Take Exponential Time to Escape Saddle Points](https://mlsanity.com/paper/1705.10412/) (2017)
- [Fast low-rank estimation by projected gradient descent: General statistical and algorithmic guarantees](https://mlsanity.com/paper/1509.03025/) (2015)
- [Continuous State-Space Models for Optimal Sepsis Treatment - a Deep Reinforcement Learning Approach](https://mlsanity.com/paper/1705.08422/) (2017)
- [On the Limitations of Unsupervised Bilingual Dictionary Induction](https://mlsanity.com/paper/1805.03620/) (2018)
- [CODER: Knowledge infused cross-lingual medical term embedding for term normalization](https://mlsanity.com/paper/2011.02947/) (2020)
- [Low-Rank Matrix Completion: A Contemporary Survey](https://mlsanity.com/paper/1907.11705/) (2019)
- [Convergence Analysis for Rectangular Matrix Completion Using Burer-Monteiro Factorization and Gradient Descent](https://mlsanity.com/paper/1605.07051/) (2016)
- [Inference for multiple heterogeneous networks with a common invariant subspace](https://mlsanity.com/paper/1906.10026/) (2019)
- [Clinical Concept Embeddings Learned from Massive Sources of Multimodal Medical Data](https://mlsanity.com/paper/1804.01486/) (2018)
- [Incoherence-Optimal Matrix Completion](https://mlsanity.com/paper/1310.0154/) (2013)
- [Matrix Completion via Max-Norm Constrained Optimization](https://mlsanity.com/paper/1303.0341/) (2013)
- [Structured Matrix Completion with Applications to Genomic Data Integration](https://mlsanity.com/paper/1504.01823/) (2015)
- [Integrating multi-source block-wise missing data in model selection](https://mlsanity.com/paper/1901.03797/) (2019)
- [Spherical Regression under Mismatch Corruption with Application to Automated Knowledge Translation](https://mlsanity.com/paper/1810.05679/) (2018)
- [Max-Norm Optimization for Robust Matrix Recovery](https://mlsanity.com/paper/1609.07664/) (2016)
- [Generalized Integrative Principal Component Analysis for Multi-Type Data with Block-Wise Missing Structure](https://mlsanity.com/paper/1808.02193/) (2018)
- [Semi-Supervised Off Policy Reinforcement Learning](https://mlsanity.com/paper/2012.04809/) (2020)
- [AWE-CM Vectors: Augmenting Word Embeddings with a Clinical Metathesaurus](https://mlsanity.com/paper/1712.01460/) (2017)

## Built on by (most cited first, 10 of 10)

- [Inference of Dependency Knowledge Graph for Electronic Health Records](https://mlsanity.com/paper/2312.15611/) (2023)
- [Representation Retrieval Learning for Heterogeneous Data Integration](https://mlsanity.com/paper/2503.09494/) (2025)
- [Low-Rank Covariance Completion for Graph Quilting with Applications to Functional Connectivity](https://mlsanity.com/paper/2209.08273/) (2022)
- [Contrastive Learning on Multimodal Analysis of Electronic Health Records](https://mlsanity.com/paper/2403.14926/) (2024)
- [Optimal Transfer Learning for Missing Not-at-Random Matrix Completion](https://mlsanity.com/paper/2503.00174/) (2025)
- [Semi-supervised Clustering Through Representation Learning of Large-scale EHR Data](https://mlsanity.com/paper/2505.20731/) (2025)
- [Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Data](https://mlsanity.com/paper/2505.24413/) (2025)
- [GeoERM: Geometry-Aware Multi-Task Representation Learning on Riemannian Manifolds](https://mlsanity.com/paper/2505.02972/) (2025)
- [Latent Factor Point Processes for Patient Representation in Electronic Health Records](https://mlsanity.com/paper/2508.20327/) (2025)
- [A Common Pipeline for Harmonizing Electronic Health Record Data for Translational Research](https://mlsanity.com/paper/2509.08553/) (2025)

## Abstract (arXiv)

Matrix completion has attracted attention in many fields, including statistics, applied mathematics, and electrical engineering. Most of the works focus on the independent sampling models under which the observed entries are sampled independently. Motivated by applications in the integration of knowledge graphs derived from multi-source biomedical data such as those from Electronic Health Records (EHR) and biomedical text, we propose the bf Block-wise bf Overlapping bf Noisy bf Matrix bf Integration (BONMI) to treat blockwise missingness of symmetric matrices representing relatedness between entity pairs. Our idea is to exploit the orthogonal Procrustes problem to align the eigenspace of the two sub-matrices, then complete the missing blocks by the inner product of the two low-rank components. Besides, we prove the statistical rate for the eigenspace of the underlying matrix, which is comparable to the rate under the independently missing assumption. Simulation studies show that the method performs well under a variety of configurations. In the real data analysis, the method is applied to two tasks: (i) the integrating of several point-wise mutual information matrices built by English EHR and Chinese medical text data, and (ii) the machine translation between English and Chinese medical concepts. Our method shows an advantage over existing methods.