Name
Abstract | ||
|---|---|---|
Compressed sensing theory explains why LASSO programs recover structured high-dimensional signals with minimax order-optimal error. Yet, the optimal choice of the program's governing parameter is often unknown in practice. It is still unclear how variation of the governing parameter impacts recovery error in compressed sensing, which is otherwise provably stable and robust. We establish a novel notion of instability in LASSO programs when the measurement matrix is identity. This is the proximal denoising setup. We prove asymptotic cusp-like behaviour of the risk as a function of the parameter choice, and illustrate the theory with numerical simulations. For example, a 0.1% underestimate of a LASSO parameter can increase the error significantly; and a 50% underestimate can cause the error to increase by a factor of 10
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">9</sup>
. We hope that revealing parameter instability regimes of LASSO programs helps to inform a practitioner's choice. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1109/SampTA45681.2019.9030982 | 2019 13th International conference on Sampling Theory and Applications (SampTA) |
Keywords | Field | DocType |
Compressed sensing,Sparse proximal denoising,Parameter instability,Convex optimization,Lasso | Noise reduction,Applied mathematics,Mathematical optimization,Minimax,Matrix (mathematics),Instability,Lasso (statistics),Compressed sensing,Mathematics | Journal |
Volume | ISBN | Citations |
abs/1810.11968 | 978-1-7281-3742-1 | 0 |
PageRank | References | Authors |
0.34 | 10 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Aaron Berk | 1 | 0 | 1.01 |
| Yaniv Plan | 2 | 1174 | 57.19 |
| Özgür Yilmaz | 3 | 685 | 51.36 |