Summary of Guaranteed Nonconvex Factorization Approach For Tensor Train Recovery, by Zhen Qin et al.
Guaranteed Nonconvex Factorization Approach for Tensor Train Recovery
by Zhen Qin, Michael B. Wakin, Zhihui Zhu
First submitted to arxiv on: 5 Jan 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Signal Processing (eess.SP); Optimization and Control (math.OC)
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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 provides a convergence guarantee for the factorization approach, specifically optimizing over the left-orthogonal TT format to enforce orthonormality among most factors using Riemannian gradient descent (RGD) on the Stiefel manifold. The authors establish local linear convergence of RGD in the TT factorization problem and show that the rate of convergence only declines linearly with increasing tensor order. They also study the sensing problem, recovering a TT format tensor from linear measurements under restricted isometry property (RIP) conditions. Assuming proper initialization through spectral initialization, they demonstrate RGD converges to the ground-truth at a linear rate, even in scenarios involving Gaussian noise. Theoretical findings are validated through experiments. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how to make better use of big data by solving a tricky math problem. They developed a new way to break down very large datasets into smaller pieces that can be easily worked with. This is important because it allows computers to quickly find patterns and relationships in the data, which is useful for things like self-driving cars and medical research. The authors tested their method on several different types of data and found that it works really well. |
Keywords
* Artificial intelligence * Gradient descent
