PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

In Search of Non-Gaussian Components of a High-Dimensional Distribution
Gilles Blanchard, Motoaki Kawanabe, Masashi Sugiyama, Vladimir Spokoiny and Klaus-Robert Müller
Journal of Machine Learning Research Volume 7, pp. 247-282, 2006.


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 essentially based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector which belongs 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.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:1340
Deposited By:Gilles Blanchard
Deposited On:28 November 2005