Subspace information criterion for nonquadratic regularizers-model selection for sparse regressors

Koji Tsuda, Masashi Sugiyama, Klaus Muller

Research output: Contribution to journalArticle

8 Citations (Scopus)


Nonquadratic regularizers, in particular the l1 norm regularizer can yield sparse solutions that generalize well. In this work we propose the generalized subspace information criterion (GSIC) that allows to predict the generalization error for this useful family of regularizers. We show that under some technical assumptions GSIC is an asymptotically unbiased estimator of the generalization error. GSIC is demonstrated to have a good performance in experiments with the l1 norm regularizer as we compare with the network information criterion (NIC) and cross- validation in relatively large sample cases. However in the small sample case, GSIC tends to fail to capture the optimal model due to its large variance. Therefore, also a biased version of GSIC is introduced, which achieves reliable model selection in the relevant and challenging scenario of high-dimensional data and few samples.

Original languageEnglish
Pages (from-to)70-80
Number of pages11
JournalIEEE Transactions on Neural Networks
Issue number1
Publication statusPublished - 2002 Jan 1
Externally publishedYes



  • Kernel methods
  • Model selection
  • Regularization
  • Sparse regressors
  • Subspace information criterion (SIC)

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Electrical and Electronic Engineering
  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Hardware and Architecture

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