Computational methods for unbiased risk estimation
Abstract/Contents
- Abstract
- In many engineering applications, one seeks to estimate, recover or reconstruct an unknown object of interest from an incomplete set of measurements. In recent years it has been shown that it is possible to recover the true object by exploiting a priori information about its structure, such as sparsity in Compressed Sensing or low-rank in Matrix Completion. However, in practice the measurements are corrupted by noise and exact recovery is not possible. A popular approach to address this issue is to solve a convex optimization problem that trades off between fidelity to the measurements and resemblance to the known structural characteristics of the true object. This tradeoff is usually controlled by a single regularization parameter. A possible criterion is to select the value of this regularization parameter by minimizing an unbiased estimate for the prediction error as a surrogate for the true prediction risk. However, evaluating this estimate requires knowledge of the regularity of the solution to the convex optimization problem with respect to the measurements. In this work we introduce a conceptual and practical framework to study the regularity of the solution to a popular class of such optimization problems. This framework leads to a disciplined approach for obtaining closed-form expressions for the derivatives of the predicted measurements that are amenable to computation. These expressions establish a connection between the geometry of the convex optimization problem and the unbiased estimate for the prediction risk.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2016 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Sing Long, Carlos A |
|---|---|
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering. |
| Primary advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Thesis advisor | Murray, Walter |
| Thesis advisor | Ryzhik, Leonid |
| Advisor | Murray, Walter |
| Advisor | Ryzhik, Leonid |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Carlos A. Sing Long. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2016. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2016 by Carlos Alberto Sing Long Collao
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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