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Sparsity and smoothness via the fused lasso

Author

Listed:
  • Robert Tibshirani
  • Michael Saunders
  • Saharon Rosset
  • Ji Zhu
  • Keith Knight

Abstract

Summary. The lasso penalizes a least squares regression by the sum of the absolute values (L1‐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 L1‐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.

Suggested Citation

  • Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
  • Handle: RePEc:bla:jorssb:v:67:y:2005:i:1:p:91-108
    DOI: 10.1111/j.1467-9868.2005.00490.x
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    File URL: https://doi.org/10.1111/j.1467-9868.2005.00490.x
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