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B0857
Title: Likelihood-based non-Gaussian and Gaussian component analysis Authors:  Benjamin Risk - Emory University (United States) [presenting]
David Matteson - Cornell University (United States)
David Ruppert - Cornell University (United States)
Abstract: Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA (PCA-ICA), which could remove important information. The problem is that interesting independent components (ICs) could be mixed in several principal components that are discarded and then these ICs cannot be recovered. We formulate a linear non-Gaussian component model with Gaussian noise components. To estimate this model, we propose likelihood component analysis (LCA), in which dimension reduction and latent variable estimation is achieved simultaneously. Our method orders components by their marginal likelihood in a manner that parallels the ordering of components by variance used in principal component analysis (PCA). We present a parametric LCA using the logistic density and a semi-parametric LCA using tilted Gaussians with cubic $B$-splines. Our algorithm is scalable to datasets common in applications (e.g. hundreds of thousands of observations across hundreds of variables with dozens of latent components). In simulations, latent components are recovered that are discarded by PCA-ICA methods. We apply our method to an fMRI experiment from the Human Connectome Project and identify artifacts missed by PCA-ICA.