In search of non-Gaussian components of a high-dimensional distribution

Gilles Blanchard, Motoaki Kawanabe, Masashi Sugiyama, Vladimir Spokoiny, Klaus Robert Müller

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

Finding non-Gaussian components of high-dimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the "non-Gaussian subspace" within a very general semi-parametric framework. Our proposed method, called NGCA (non-Gaussian component analysis), is based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector belonging to the low dimensional non-Gaussian target subspace, up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method.

Original languageEnglish
Pages (from-to)247-282
Number of pages36
JournalJournal of Machine Learning Research
Volume7
Publication statusPublished - 2006 Feb
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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