PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Fast Kernel ICA using an Approximate Newton Method
Hao Shen, stefanie jegelka and Arthur Gretton
In: AISTATS 2007, 21 Mar - 24 Mar 2007, San Juan Puerto Rico.

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.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:3141
Deposited By:Arthur Gretton
Deposited On:21 December 2007