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Title: Marginalization of latent variables for correlated data Authors:  Mengyang Gu - University of California, Santa Barbara (United States) [presenting]
Abstract: Marginalization of latent variables for correlated outcomes is discussed, including multiple time series, spatio-temporal processes, and functional data. We highlight two features of marginalization. First, we show marginalizing correlated latent variables leads to an efficient estimation of model parameters. As an example, we will introduce generalized probabilistic principal component analysis (GPPCA) to study the latent factor model for multiple correlated outcomes. The method generalizes the previous probabilistic formulation of principal component analysis (PPCA) by providing the closed-form maximum marginal likelihood estimator of the factor loadings and other parameters, where each factor is modeled by a Gaussian process. Second, we show marginalization leads to scalable computation for modeling a massive number of correlated data by Gaussian processes. Numerical studies of simulated and real data confirm the excellent finite-sample performance of the proposed approach.