An iterative hard thresholding estimator for low rank matrix recovery with explicit limiting distribution
- We consider the problem of low rank matrix recovery in a stochastically noisy high-dimensional setting. We propose a new estimator for the low rank matrix, based on the iterative hard thresholding method, that is computationally efficient and simple. We prove that our estimator is optimal in terms of the Frobenius risk and in terms of the entry-wise risk uniformly over any change of orthonormal basis, allowing us to provide the limiting distribution of the estimator. When the design is Gaussian, we prove that the entry-wise bias of the limiting distribution of the estimator is small, which is of interest for constructing tests and confidence sets for low-dimensional subsets of entries of the low rank matrix.
| Author details: | Alexandra CarpentierORCiDGND, Arlene K. H. Kim |
|---|---|
| DOI: | https://doi.org/10.5705/ss.202016.0103 |
| ISSN: | 1017-0405 |
| ISSN: | 1996-8507 |
| Title of parent work (English): | Statistica Sinica |
| Publisher: | Statistica Sinica, Institute of Statistical Science, Academia Sinica |
| Place of publishing: | Taipei |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2018 |
| Publication year: | 2018 |
| Release date: | 2021/11/12 |
| Tag: | High dimensional statistical inference; inverse problem; limiting distribution; low rank matrix recovery; numerical methods; uncertainty quantification |
| Volume: | 28 |
| Issue: | 3 |
| Number of pages: | 23 |
| First page: | 1371 |
| Last Page: | 1393 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Green Open-Access |
