  We study optimization methods for solving the maximum likelihood formulation
of independent component analysis (ICA). We consider both the the problem
constrained to white signals and the unconstrained problem. The Hessian of the
objective function is costly to compute, which renders Newton's method
impractical for large data sets. Many algorithms proposed in the literature can
be rewritten as quasi-Newton methods, for which the Hessian approximation is
cheap to compute. These algorithms are very fast on simulated data where the
linear mixture assumption really holds. However, on real signals, we observe
that their rate of convergence can be severely impaired. In this paper, we
investigate the origins of this behavior, and show that the recently proposed
Preconditioned ICA for Real Data (Picard) algorithm overcomes this issue on
both constrained and unconstrained problems.
