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A Majorization-Minimization Gauss-Newton Method for 1-Bit Matrix Completion.

Xiaoqian Liu1, Xu Han2, Eric C Chi3

  • 1Department of Statistics, University of California, Riverside.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|August 26, 2025
PubMed
Summary
This summary is machine-generated.

We introduce Majorization-Minimization Gauss-Newton (MMGN), a new method for 1-bit matrix completion. MMGN efficiently estimates low-rank matrices from binary data, offering accurate and fast results compared to existing techniques.

Keywords:
Binary observationsConstrained least squaresLow-rank matrixMaximum likelihood estimate

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Area of Science:

  • Machine Learning
  • Optimization
  • Data Science

Background:

  • 1-bit matrix completion involves estimating low-rank matrices from limited binary data.
  • Existing methods face challenges with accuracy, speed, and data sensitivity.

Purpose of the Study:

  • To introduce a novel and efficient method for 1-bit matrix completion.
  • To improve estimation accuracy and computational speed for binary matrix completion tasks.

Main Methods:

  • The Majorization-Minimization Gauss-Newton (MMGN) method is proposed.
  • It reformulates the problem into a sequence of low-rank matrix completion subproblems.
  • Subproblems are solved using factorization and Gauss-Newton optimization.

Main Results:

  • MMGN provides estimates comparable or superior in accuracy to existing methods.
  • The method demonstrates significant speed improvements, especially with sparse data.
  • MMGN shows reduced sensitivity to the 'spikiness' of the underlying matrix.

Conclusions:

  • MMGN offers a computationally advantageous approach to 1-bit matrix completion.
  • The method is robust and efficient for estimating low-rank matrices from binary observations.
  • MMGN presents a valuable alternative for various data completion applications.