Maximum Likelihood ICA
Éric Moreau, Tülay Adalı · 2013
In this chapter, the authors present mutual information rate as the cost that implies the use of all three types of diversity at the same time, non-Gaussianity, sample-dependence and non-circularity. For a given set of observations, one can write the likelihood function to maximize, which is equivalent to the minimization of the mutual information cost. The authors introduce a number of approaches for achieving independent component analysis (ICA) using maximum likelihood (ML), and study those that assume an unconstrained demixing matrix and constrain the demixing matrix to be unitary. Finally, the authors deal with an important tool, the decoupling trick, which enables isolating the update of each source without having to constrain the demixing matrix to be unitary. The authors also deal with the complex entropy bound minimization (EBM) algorithm that uses a semi-parametric approach for approximating the density along with the decoupling trick for improved performance.