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Computationally efficient multilevel Gaussian process regression for functional data observed under completely or partially regular sampling designs
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DOI：10.1007/s11749-025-00996-4.png)
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Abstract
En 中文
Gaussian process regression is a common method for flexible yet fully probabilistic nonlinear regression. A frequent obstacle is its computational complexity, which scales poorly with the number of observations. The problem intensifies when Gaussian process models are applied simultaneously to multiple functions. We consider a multilevel Gaussian process regression model in which a common mean function and subject-specific deviations are jointly modeled as latent Gaussian processes. We derive exact, analytic, and computationally efficient expressions for the log-likelihood and the conditional posterior distributions when observations are sampled on either a completely or partially regular grid. Without using approximations, these expressions enable us to fit the model to large data sets that are currently computationally inaccessible with a standard implementation. We show through a simulation study that our analytic expressions are several orders of magnitude faster than a standard implementation, and we provide an implementation in the probabilistic programming language Stan.
Keywords:
Bayesian statistics
Computational statistics
Functional data analysis
Gaussian process regression