Abstract:
|
We introduce a general framework of Gaussian stochastic process (GaSP) models to capture multiple functional data observations with a fast, exact algorithm in large-scale data. GaSP models are widely used in modeling functional data, with applications in emulation, interpolation, classification, and uncertainty quantification. While GaSP is flexible from a modeling standpoint, the major limitation is in the evaluation of the likelihood, which is O(n^3), where n is the sample size. We propose a general class of nonseparable GaSP models, in which the computation is linear to the sample size and the evaluation of the likelihood is exact, i.e. without assuming that either the covariance or precision matrices is sparse or low-rank. We show that linear regression and separable GaSP models are special cases of the proposed nonseparable GaSP. The advantages of our nonseparable GaSP model with objective Bayesian analysis are illustrated in an epigenetic application in which the goal is to interpolate unobserved methylation levels.
|