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Fast Kernel ICA using an Approximate Newton Method

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Jegelka,  S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Shen, H., Jegelka, S., & Gretton, A. (2007). Fast Kernel ICA using an Approximate Newton Method. In M. Meila, & X. shen (Eds.), Artificial Intelligence and Statistics, 21-24 March 2007, San Juan, Puerto Rico (pp. 476-483). Madison, WI, USA: International Machine Learning Society.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CE7B-0
Abstract
Recent approaches to independent component analysis (ICA) have used kernel independence measures to obtain very good performance, particularly where classical methods experience difficulty (for instance, sources with near-zero kurtosis). We present Fast Kernel ICA (FastKICA), a novel optimisation technique for one such kernel independence measure, the Hilbert-Schmidt independence criterion (HSIC). Our search procedure uses an approximate Newton method on the special orthogonal group, where we estimate the Hessian locally about independence. We employ incomplete Cholesky decomposition to efficiently compute the gradient and approximate Hessian. FastKICA results in more accurate solutions at a given cost compared with gradient descent, and is relatively insensitive to local minima when initialised far from independence. These properties allow kernel approaches to be extended to problems with larger numbers of sources and observations. Our method is competitive with other modern and classical ICA approaches in both speed and accuracy.