We then turn our focus to more general predictor spaces and scaling to high-dimensional datasets. Here, the predictor space could represent not only time, but also space or other factors. Our proposed Bayesian nonparametric covariance regression framework harnesses a latent factor model representation. In particular, the predictor-dependent factor loadings are characterized as a sparse combination of a collection of unknown dictionary functions (e.g, Gaussian process random functions). The induced predictor-dependent covariance is then a regularized quadratic function of these dictionary elements. Our proposed framework leads to a highly-flexible, but computationally tractable formulation with simple conjugate posterior updates that can readily handle missing data. Theoretical properties are discussed and the methods are illustrated through an application to the Google Flu Trends data and the task of word classification based on single-trial MEG data.
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