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

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.