A new perspective on independent component analysis

The paper examines the performance of the independent component analysis (ICA) which represents random vectors X by vectors X˜ whose components are linear forms of independent random variables. The representation holds exactly or asymptotically in tails for Gaussian and non-Gaussian vectors with special characteristic functions or Gaussian, translation, and non-Gaussian vectors with independent tails. However, the distributions of X˜ and its target vector X differ for a board range of non-Gaussian vectors. This statement is supported by numerical examples and theoretical arguments. It is also shown that the ICA representation X˜ is approximately Gaussian for high dimensional vectors.