Title: Independent Component Analysis via Energy-based and Kernel-based Mutual Dependence Measures,
Abstract: We apply both distance-based (Jin and Matteson, 2017) and kernel-based
(Pfister et al., 2016) mutual dependence measures to independent component
analysis (ICA), and generalize dCovICA (Matteson and Tsay, 2017) to MDMICA,
minimizing empirical dependence measures as an objective function in both
deflation and parallel manners. Solving this minimization problem, we introduce
Latin hypercube sampling (LHS) (McKay et al., 2000), and a global optimization
method, Bayesian optimization (BO) (Mockus, 1994) to improve the initialization
of the Newton-type local optimization method. The performance of MDMICA is
evaluated in various simulation studies and an image data example. When the ICA
model is correct, MDMICA achieves competitive results compared to existing
approaches. When the ICA model is misspecified, the estimated independent
components are less mutually dependent than the observed components using
MDMICA, while they are prone to be even more mutually dependent than the
observed components using other approaches.