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Abstract:
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Gaussian processes are widely used for the analysis of spatial data due to their nonparametric flexibility and ability to quantify uncertainty, and recently developed scalable approximations have facilitated application to massive datasets. For multivariate outcomes, the linear model of coregionalization combines dimension reduction with spatial correlation. However, these real-valued latent representations are not sparse and are difficult to interpret. We propose a non-negative factorization (NPF) via log-Gaussian processes that naturally encourages sparsity in both latent factors and loadings, while maintaining probabilistic uncertainty quantification. We illustrate the utility of NPF with application to spatial gene expression data.
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