Adaptive basis expansion via l1 trend filtering

Daeju Kim, Shuichi Kawano, Yoshiyuki Ninomiya

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We propose a new approach for nonlinear regression modeling by employing basis expansion for the case where the underlying regression function has inhomogeneous smoothness. In this case, conventional nonlinear regression models tend to be over- or underfitting, where the function is more or less smoother, respectively. First, the underlying regression function is roughly approximated with a locally linear function using an l1 penalized method, where this procedure is executed by extending an algorithm for the fused lasso signal approximator. We then extend the fused lasso signal approximator and develop an algorithm. Next, the residuals between the locally linear function and the data are used to adaptively prepare the basis functions. Finally, we construct a nonlinear regression model with these basis functions along with the technique of a regularization method. To select the optimal values of the tuning parameters for the regularization method, we provide an explicit form of the generalized information criterion. The validity of our proposed method is then demonstrated through several numerical examples.

Original languageEnglish
Pages (from-to)1005-1023
Number of pages19
JournalComputational Statistics
Issue number5
Publication statusPublished - Oct 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics


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