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Title: A Bayesian nonparametric approach to factor analysis Authors:  Remi Piatek - University of Copenhagen (Denmark) [presenting]
Abstract: A new approach is introduced for the inference of non-Gaussian factor models based on Bayesian nonparametric methods. It relaxes the usual normality assumption on the latent factors, widely used in practice, which is too restrictive in many settings. The approach, on the contrary, does not impose any particular assumptions on the shape of the distribution of the factors, but still secures the basic requirements for the identification of the model. We design a new sampling scheme based on marginal data augmentation for the inference of mixtures of normals with location and scale restrictions. This approach is augmented by the use of a retrospective sampler, to allow for the inference of a constrained Dirichlet process mixture model for the distribution of the latent factors. We carry out a simulation study to illustrate the methodology and demonstrate its benefits. The sampler is very efficient in recovering the distribution of the factors, and only generates models that fulfill the identification requirements. A real data example illustrates the applicability of the approach.