Summary of Low-rank Bayesian Matrix Completion Via Geodesic Hamiltonian Monte Carlo on Stiefel Manifolds, by Tiangang Cui and Alex Gorodetsky
Low-rank Bayesian matrix completion via geodesic Hamiltonian Monte Carlo on Stiefel manifolds
by Tiangang Cui, Alex Gorodetsky
First submitted to arxiv on: 27 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Numerical Analysis (math.NA); Computation (stat.CO); Methodology (stat.ME)
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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 This paper presents a novel approach for efficient computation of low-rank Bayesian matrix completion while quantifying uncertainty. A new prior model is designed based on singular-value-decomposition (SVD) parametrization of low-rank matrices, enforcing orthogonality in factor matrices through Stiefel manifold constraints. A geodesic Hamiltonian Monte Carlo algorithm is developed for generating posterior samples of SVD factor matrices, resolving sampling difficulties encountered by standard Gibbs samplers for two-matrix factorization used in matrix completion. The approach allows for sampling with more general likelihoods than typical Gaussian assumptions and demonstrates improved accuracy on real-world benchmark problems. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper introduces a new way to do something called Bayesian matrix completion. It’s like filling in missing information, but instead of just guessing, it uses math and statistics to make sure the answer is right. They came up with a new idea for how to do this by using something called SVD, which helps keep the answers organized and correct. Then they created an algorithm to find the answers, and tested it on some real-world problems. It worked really well! |
