Fused Lasso Additive Model

Ashley Petersen, Daniela Witten, Noah Simon

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We consider the problem of predicting an outcome variable using p covariates that are measured on n independent observations, in a setting in which additive, flexible, and interpretable fits are desired. We propose the fused lasso additive model (FLAM), in which each additive function is estimated to be piecewise constant with a small number of adaptively chosen knots. FLAM is the solution to a convex optimization problem, for which a simple algorithm with guaranteed convergence to a global optimum is provided. FLAM is shown to be consistent in high dimensions, and an unbiased estimator of its degrees of freedom is proposed. We evaluate the performance of FLAM in a simulation study and on two datasets. Supplemental materials are available online, and the R package flam is available on CRAN.

Original languageEnglish (US)
Pages (from-to)1005-1025
Number of pages21
JournalJournal of Computational and Graphical Statistics
Volume25
Issue number4
DOIs
StatePublished - Oct 1 2016

Keywords

  • Additive model
  • Feature selection
  • High-dimensional
  • Nonparametric regression
  • Piecewise constant
  • Sparsity

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