389. Faster Randomized Methods for Orthogonality Constrained Problems
Invited abstract in session TC-11: Advances in Manifold and Conic Optimization, stream Riemannian Manifold and Conic Optimization.
Tuesday, 14:00-16:00Room: B100/5017
Authors (first author is the speaker)
| 1. | Boris Shustin
|
| SC, RAL-STFC | |
| 2. | Haim Avron
|
| Tel Aviv University |
Abstract
Recent literature has advocated the use of randomized methods for accelerating the solution of various matrix problems arising in machine learning and data science. One popular strategy for leveraging randomization in numerical linear algebra is to use it as a way to reduce problem size. However, methods based on this strategy lack sufficient accuracy for some applications. Randomized preconditioning is another approach for leveraging randomization in numerical linear algebra, which provides higher accuracy. The main challenge in using randomized preconditioning is the need for an underlying iterative method, thus, randomized preconditioning so far has been applied almost exclusively to solving regression problems and linear systems. In this talk, we show how to expand the application of randomized preconditioning to another important set of problems prevalent in machine learning: optimization problems with (generalized) orthogonality constraints. We demonstrate our approach, which is based on the framework of Riemannian optimization and Riemannian preconditioning, on the problem of computing the dominant canonical correlations.
Keywords
- Computational linear algebra
- Large-scale optimization
- Optimization for learning and data analysis
Status: accepted
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