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
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
Numerical examples demonstrate the usefulness of our method.