Summary of Optimization Without Retraction on the Random Generalized Stiefel Manifold, by Simon Vary et al.
Optimization without Retraction on the Random Generalized Stiefel Manifold
by Simon Vary, Pierre Ablin, Bin Gao, P.-A. Absil
First submitted to arxiv on: 2 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC); Machine Learning (stat.ML)
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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 The proposed method addresses optimization problems on the generalized Stiefel manifold, a set of matrices satisfying specific conditions. These problems appear in applications like canonical correlation analysis (CCA), independent component analysis (ICA), and generalized eigenvalue problem (GEVP). The conventional approach involves iterative methods that require a fully formed matrix B. In contrast, the proposed method is a cheap stochastic iterative technique that solves these optimization problems while having only random estimates of B. This method produces iterations that converge to critical points on the generalized Stiefel manifold in expectation, with lower per-iteration cost and comparable convergence rates to Riemannian optimization counterparts. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper proposes a new way to solve certain math problems involving matrices. These problems show up in things like image recognition and data analysis. Usually, people use special methods that need the whole matrix B to work. But this method is different – it’s cheaper and uses only parts of the matrix B. It does this by making guesses about what the matrix should look like and then adjusting its answers based on how well they fit. The results are good, and the new method can be used for things like recognizing patterns in data. |
Keywords
» Artificial intelligence » Optimization
