Topics in matrix inference
Abstract/Contents
- Abstract
- Two topics in matrix inference are considered: matrix denoising and matrix organization. In matrix denoising, one attempts to recover an unknown matrix $X$ from a single noisy observation $Y=X+Z$, where $Z$ is a noise matrix with independent, identically distributed entries. It is shown that random matrix theory delivers simple, convincing answers to a range of fundamental questions, such as the minimax risk of matrix denoising by singular value soft thresholding, the location of the optimal singular value threshold and the shape of the optimal singular value shrinker. In matrix organization, one attempts to recover the latent structure of the row set of the column set of a matrix, such that matrix entries can be reliably predicted from close-by entries. We propose a self-contained framework for matrix organization and subsequent sampling, approximation and compression.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2014 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Gavish, Matan |
|---|---|
| Associated with | Stanford University, Department of Statistics. |
| Primary advisor | Coifman, Ronald R. (Ronald Raphaël) |
| Primary advisor | Donoho, David Leigh |
| Thesis advisor | Coifman, Ronald R. (Ronald Raphaël) |
| Thesis advisor | Donoho, David Leigh |
| Thesis advisor | Johnstone, I. M |
| Advisor | Johnstone, I. M |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Matan Gavish. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2014. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2014 by Matan Gavish
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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