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Abstract:
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The Bayesian Multi-Study Factor model (De Vito et al., 2019, 2018) handles multiple high-dimensional studies simultaneously, achieving two goals: a) to capture the component shared across studies and b) to identify the sources of variation unique to each study. In this work, we propose a novel sparse Bayesian Multi-study Factor model by adopting a latent factor regression approach. This generalization recovers a covariance structure that identifies the common and study-specific covariances, keeping track of the observed variables, such as the demographic information. We consider spike and slab sparse priors (local and non-local) to detect the dimension of the latent factors. A user-defined prior dispersion for the regression coefficient accounts for population structure and other demographic characteristics for the subjects. We assess the characteristic of our method by a range of simulations settings, clarifying the benefit of using our model. We illustrate the advantages of the proposed method through a high dimensional application, the nutritional data application.
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