| | |
| | |
Stat |
Members: 3643 Articles: 2'488'730 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
Optimal Adaptive Matrix Completion | Ilqar ramazanli
; Barnabas Poczos
; | Date: |
6 Feb 2020 | Abstract: | We study the problem of exact completion for $m imes n$ sized matrix of
rank r with the adaptive sampling method. We introduce a relation of the exact
completion problem with the sparsest vector of column and row spaces (which we
call sparsity-number here). Using this relation, we propose matrix completion
algorithms that exactly recovers the target matrix. These algorithms are
superior to previous works in two important ways. First, our algorithms exactly
recover $mu_0$-coherent column space matrices by probability at least
$1-epsilon$ using much smaller observations complexity than -
$mathcal{O}(mu_0 rn mathrm{log}frac{r}{epsilon})$ - the state of art.
Specifically, many of the previous adaptive sampling methods require to observe
the entire matrix when the column space is highly coherent. However, we show
that our method is still able to recover this type of matrices by observing a
small fraction of entries under many scenarios. Second, we propose an exact
completion algorithm, which requires minimal pre-information as either row or
column space is not being highly coherent. We provide an extension of these
algorithms that is robust to sparse random noise. Besides, we propose an
additional low-rank estimation algorithm that is robust to any small noise by
adaptively studying the shape of column space. At the end of the paper, we
provide experimental results that illustrate the strength of the algorithms
proposed here. | Source: | arXiv, 2002.2431 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |