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

Natural Selection, Irrationality and Monopolistic Competition

This paper builds an evolutionary model of an industry where firms produce differentiated products. Firms have different average cost functions and different demand functions. Firms are assumed to be totally irrational in the sense that firms enter the industry regardless of the existence of profits; firms' outputs are randomly determined rather than generated from profit maximization problems; and firms exit the industry if their wealth is negative. It shows that without purposive profit maximization assumption, monopolistic competition still evolves in the long run. The only long run survivors are those that possess the most efficient technology, face the most favorable market conditions and produce at their profit maximizing outputs. This paper modifies and supports the classic argument for the derivation of monopolistic competition.Evolution, Natural Selection, Irrationality, Monopolistic Competition, Survival of the Fittest, Market Rationality