scholarly journals Exact post-selection inference for the generalized lasso path

2018 ◽  
Vol 12 (1) ◽  
pp. 1053-1097 ◽  
Author(s):  
Sangwon Hyun ◽  
Max G’Sell ◽  
Ryan J. Tibshirani
Keyword(s):  
Generalized Lasso

scholarly journals The solution path of the generalized lasso

2011 ◽  
Vol 39 (3) ◽  
pp. 1335-1371 ◽  
Author(s):  
Ryan J. Tibshirani ◽  
Jonathan Taylor
Keyword(s):  
Solution Path ◽  
Generalized Lasso

Sensitivity of ℓ1 minimization to parameter choice

2020 ◽  
Author(s):  
Aaron Berk ◽  
Yaniv Plan ◽  
Özgür Yilmaz
Keyword(s):  
Real Data ◽  
Optimal Choice ◽  
High Dimensional ◽  
Parameter Choice ◽  
Optimal Error ◽  
Governing Parameter ◽  
ℓ1 Minimization ◽  
Optimal Value ◽  
Generalized Lasso ◽  
Common Technique

Abstract The use of generalized Lasso is a common technique for recovery of structured high-dimensional signals. There are three common formulations of generalized Lasso; each program has a governing parameter whose optimal value depends on properties of the data. At this optimal value, compressed sensing theory explains why Lasso programs recover structured high-dimensional signals with minimax order-optimal error. Unfortunately in practice, the optimal choice is generally unknown and must be estimated. Thus, we investigate stability of each of the three Lasso programs with respect to its governing parameter. Our goal is to aid the practitioner in answering the following question: given real data, which Lasso program should be used? We take a step towards answering this by analysing the case where the measurement matrix is identity (the so-called proximal denoising setup) and we use $\ell _{1}$ regularization. For each Lasso program, we specify settings in which that program is provably unstable with respect to its governing parameter. We support our analysis with detailed numerical simulations. For example, there are settings where 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 $10^{9}$.

The Generalized LASSO

2004 ◽  
Vol 15 (1) ◽  
pp. 16-28 ◽  
Author(s):  
V. Roth
Keyword(s):  
Generalized Lasso

scholarly journals Safe Feature Screening for Generalized LASSO

2018 ◽  
Vol 40 (12) ◽  
pp. 2992-3006 ◽  
Author(s):  
Shaogang Ren ◽  
Shuai Huang ◽  
Jieping Ye ◽  
Xiaoning Qian
Keyword(s):  
Feature Screening ◽  
Generalized Lasso

A modified generalized lasso algorithm to detect local spatial clusters for count data

2018 ◽  
Vol 102 (4) ◽  
pp. 537-563 ◽  
Author(s):  
Hosik Choi ◽  
Eunjung Song ◽  
Seung-sik Hwang ◽  
Woojoo Lee
Keyword(s):  
Count Data ◽  
Spatial Clusters ◽  
Generalized Lasso

scholarly journals Generalized LASSO with under-determined regularization matrices

2016 ◽  
Vol 127 ◽  
pp. 239-246 ◽  
Author(s):  
Junbo Duan ◽  
Charles Soussen ◽  
David Brie ◽  
Jérôme Idier ◽  
Mingxi Wan ◽  
...  
Keyword(s):  
Generalized Lasso
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