Sparsity and smoothness via the fused lasso

• 成果类型: Article
• 署名作者: Tibshirani, R; Saunders, M; Rosset, S; Zhu, J; Knight, K
• 署名单位: Stanford University; International Business Machines (IBM); IBM USA; University of Michigan System; University of Michigan; University of Toronto
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2005.00490.x
• 发表日期: 2005
• 页码: 91-108
• 关键词: gene-expression; cancer; regression; shrinkage

摘要

The lasso penalizes a least squares regression by the sum of the absolute values (L-1-norm) of the coefficients. The form of this penalty encourages sparse solutions (with many coefficients equal to 0). We propose the 'fused lasso', a generalization that is designed for problems with features that can be ordered in some meaningful way. The fused lasso penalizes the L-1-norm of both the coefficients and their successive differences. Thus it encourages sparsity of the coefficients and also sparsity of their differences-i.e. local constancy of the coefficient profile. The fused lasso is especially useful when the number of features p is much greater than N, the sample size. The technique is also extended to the 'hinge' loss function that underlies the support vector classifier. We illustrate the methods on examples from protein mass spectroscopy and gene expression data.