Modeling Covariate Effects in Group Independent Component Analysis with Applications to Functional Magnetic Resonance Imaging

Independent component analysis (ICA) is a powerful computational tool for separating independent source signals from their linear mixtures. ICA has been widely applied in neuroimaging studies to identify and characterize underlying brain functional networks. An important goal in such studies is to assess the effects of subjects' clinical and demographic covariates on the spatial distributions of the functional networks. Currently, covariate effects are not incorporated in existing group ICA decomposition methods. Hence, they can only be evaluated through ad-hoc approaches which may not be accurate in many cases. In this paper, we propose a hierarchical covariate ICA model that provides a formal statistical framework for estimating and testing covariate effects in ICA decomposition. A maximum likelihood method is proposed for estimating the covariate ICA model. We develop two expectation-maximization (EM) algorithms to obtain maximum likelihood estimates. The first is an exact EM algorithm, which has analytically tractable E-step and M-step. Additionally, we propose a subspace-based approximate EM, which can significantly reduce computational time while still retain high model-fitting accuracy. Furthermore, to test covariate effects on the functional networks, we develop a voxel-wise approximate inference procedure which eliminates the needs of computationally expensive covariance estimation. The performance of the proposed methods is evaluated via simulation studies. The application is illustrated through an fMRI study of Zen meditation.Comment: 36 pages, 5 figure

Rational Solutions of the H3 and Q1 Models in the ABS Lattice List

In the paper we present rational solutions for the H3 and Q1 models in the Adler-Bobenko-Suris lattice list. These solutions are in Casoratian form and are generated by considering difference equation sets satisfied by the basic Casoratian column vector