Tensor train completion: local recovery guarantees via Riemannian optimization
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912314431635456 |
|---|---|
| author | Budzinskiy, Stanislav Zamarashkin, Nikolai |
| author_facet | Budzinskiy, Stanislav Zamarashkin, Nikolai |
| contents | In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_03975 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Tensor train completion: local recovery guarantees via Riemannian optimization Budzinskiy, Stanislav Zamarashkin, Nikolai Numerical Analysis Machine Learning In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees. |
| title | Tensor train completion: local recovery guarantees via Riemannian optimization |
| topic | Numerical Analysis Machine Learning |
| url | https://arxiv.org/abs/2110.03975 |