A Path Algorithm for the Fused Lasso Signal Approximator
The Lasso is a very well-known penalized regression model, which adds an L 1 penalty with parameter λ 1 on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L 1 penalty with parameter λ 2 on the difference of neighboring coefficients, assuming...
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          | Published in | Journal of computational and graphical statistics Vol. 19; no. 4; pp. 984 - 1006 | 
|---|---|
| Main Author | |
| Format | Journal Article | 
| Language | English | 
| Published | 
        Alexandria
          Taylor & Francis
    
        01.12.2010
     JCGS Management Committee of the American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America Taylor & Francis Ltd  | 
| Subjects | |
| Online Access | Get full text | 
| ISSN | 1061-8600 1537-2715  | 
| DOI | 10.1198/jcgs.2010.09208 | 
Cover
| Abstract | The Lasso is a very well-known penalized regression model, which adds an L
1
penalty with parameter λ
1
on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L
1
penalty with parameter λ
2
on the difference of neighboring coefficients, assuming there is a natural ordering. In this article, we develop a path algorithm for solving the Fused Lasso Signal Approximator that computes the solutions for all values of λ
1
and λ
2
. We also present an approximate algorithm that has considerable speed advantages for a moderate trade-off in accuracy. In the Online Supplement for this article, we provide proofs and further details for the methods developed in the article. | 
    
|---|---|
| AbstractList | The Lasso is a very well-known penalized regression model, which adds an L
1
penalty with parameter λ
1
on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L
1
penalty with parameter λ
2
on the difference of neighboring coefficients, assuming there is a natural ordering. In this article, we develop a path algorithm for solving the Fused Lasso Signal Approximator that computes the solutions for all values of λ
1
and λ
2
. We also present an approximate algorithm that has considerable speed advantages for a moderate trade-off in accuracy. In the Online Supplement for this article, we provide proofs and further details for the methods developed in the article. The Lasso is a very well-known penalized regression model, which adds an L^sub 1^ penalty with parameter ...^sub 1^ on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L^sub 1^ penalty with parameter ...^sub 2^ on the difference of neighboring coefficients, assuming there is a natural ordering. This article develops a path algorithm for solving the Fused Lasso Signal Approximator that computes the solutions for all values of ...^sub 1^ and ...^sub 2^. It also presents an approximate algorithm that has considerable speed advantages for a moderate trade-off in accuracy. (ProQuest: ... denotes formulae/symbols omitted.) The Lasso is a very well-known penalized regression model, which adds an L₁ penalty with parameter λ₁ on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L₁ penalty with parameter λ₂ on the difference of neighboring coefficients, assuming there is a natural ordering. In this article, we develop a path algorithm for solving the Fused Lasso Signal Approximator that computes the solutions for all values of λ₁ and λ₂. We also present an approximate algorithm that has considerable speed advantages for a moderate trade-off in accuracy. In the Online Supplement for this article, we provide proofs and further details for the methods developed in the article.  | 
    
| Author | Hoefling, Holger | 
    
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| Snippet | The Lasso is a very well-known penalized regression model, which adds an L
1
penalty with parameter λ
1
on the coefficients to the squared error loss function.... The Lasso is a very well-known penalized regression model, which adds an L₁ penalty with parameter λ₁ on the coefficients to the squared error loss function.... The Lasso is a very well-known penalized regression model, which adds an L^sub 1^ penalty with parameter ...^sub 1^ on the coefficients to the squared error...  | 
    
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| SubjectTerms | Accuracy Algorithms Approximation Chromosomes Coefficients Comparative genomic hybridization Componentwise operations Convex optimization Datasets Identifiability Image reconstruction Lasso Lasso, LARS, and L₁ Regularization Mathematical independent variables Mathematical models Mathematical problems Penalized regression Regression analysis Studies Vertices  | 
    
| Title | A Path Algorithm for the Fused Lasso Signal Approximator | 
    
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