mlsanityData to 7 Oct 2026

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

arXiv 2105.10360 ↗First posted 21 May 2021stat.ML cs.LG math.STcited by 10

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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.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 30 of its 108 references that are in the map. First posted on arXiv 21 May 2021.

Builds on

30 of 108 references.

References · 30

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18 more
  1. 2017Gradient Descent Can Take Exponential Time to Escape Saddle Pointscited by 74
  2. 2015Fast low-rank estimation by projected gradient descent: General statistical and algorithmic guaranteescited by 68
  3. 2017Continuous State-Space Models for Optimal Sepsis Treatment - a Deep Reinforcement Learning Approachcited by 68
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Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 1; 2024: 1; 2025: 7.

10 papers.

  1. 2023Inference of Dependency Knowledge Graph for Electronic Health Recordscited by 5
  2. 2025Representation Retrieval Learning for Heterogeneous Data Integrationcited by 5
  3. 2022Low-Rank Covariance Completion for Graph Quilting with Applications to Functional Connectivitycited by 4
  4. 2024Contrastive Learning on Multimodal Analysis of Electronic Health Recordscited by 2
  5. 2025Optimal Transfer Learning for Missing Not-at-Random Matrix Completioncited by 2
  6. 2025Semi-supervised Clustering Through Representation Learning of Large-scale EHR Datacited by 1
  7. 2025Multi-task Learning for Heterogeneous Multi-source Block-Wise Missing Datacited by 1
  8. 2025GeoERM: Geometry-Aware Multi-Task Representation Learning on Riemannian Manifoldscited by 0
  9. 2025Latent Factor Point Processes for Patient Representation in Electronic Health Recordscited by 0
  10. 2025A Common Pipeline for Harmonizing Electronic Health Record Data for Translational Researchcited by 0