Computationally efficient multilevel Gaussian process regression for functional data observed under completely or partially regular sampling designs
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Adam Gorm Hoffmann [1] ; Claus Thorn Ekstrøm [1] ; Andreas Kryger Jensen [1]
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[1] University of Copenhagen
University of Copenhagen
Dinamarca
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 35, Nº. 1, 2026, págs. 211-231
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
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.
