Summary of Predictive Low Rank Matrix Learning Under Partial Observations: Mixed-projection Admm, by Dimitris Bertsimas and Nicholas A. G. Johnson
Predictive Low Rank Matrix Learning under Partial Observations: Mixed-Projection ADMM
by Dimitris Bertsimas, Nicholas A. G. Johnson
First submitted to arxiv on: 18 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A machine learning framework is proposed to learn partially observed matrices under the low rank assumption, leveraging fully observed side information that depends linearly on the true matrix. This generalizes the Matrix Completion problem, crucial in recommendation systems, signal processing, system identification, and image denoising. The problem is formulated as an optimization balance between fit and predictability, with a mixed-projection reformulation and semidefinite cone relaxation. An alternating direction method of multipliers algorithm is designed for efficient solution generation, achieving high-quality feasible solutions. Numerical results show the algorithm outperforms benchmarks in synthetic data, with significant improvements in objective value and reconstruction error. The runtime is competitive or superior to benchmark methods. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A team of researchers developed a new way to learn about partially seen matrices using extra information that’s related to the true matrix. This helps solve problems like recommending things you might like or removing noise from images. They turned this problem into an optimization challenge, where they balance how well their answer fits the known pieces with how good it is at predicting the missing parts. They came up with a new algorithm to solve this problem quickly and accurately. Their results show that their method works better than other approaches in some cases. |
Keywords
» Artificial intelligence » Image denoising » Machine learning » Optimization » Signal processing » Synthetic data
