Report
Efficient constrained Gaussian process approximation using elliptical slice sampling
| العنوان: | Efficient constrained Gaussian process approximation using elliptical slice sampling |
|---|---|
| المؤلفون: | Maatouk, Hassan, Rullière, Didier, Bay, Xavier |
| المساهمون: | Analyse, Géométrie et Modélisation (AGM - UMR 8088), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom Paris (IMT), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom Paris (IMT)-Institut Mines-Télécom Paris (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA) |
| المصدر: | https://hal.science/hal-04496474 ; 2024. |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2024 |
| المجموعة: | Université Paris Seine: ComUE (HAL) |
| مصطلحات موضوعية: | Elliptical slice sampling, nonparametric regression, shape constraints, smooth relaxation, Toeplitz, [STAT]Statistics [stat] |
| الوصف: | In this paper, Bayesian shape-restricted function estimation using constrained Gaussian processes (GPs) is revisited. The finite-dimensional Gaussian process approximation proposed in [H. Maatouk and X. Bay. Gaussian process emulators for computer experiments with inequality constraints. Mathematical Geosciences, 49(5):557–582, 2017] is considered. This approximation verifies a wide range of shape constraints such as monotonicity, convexity and boundedness constraints in the entire domain. Through this approach, shape constraints are reformulated as equivalent linear inequality constraints on the basis coefficients. To generate a sample from the resulting constrained posterior distribution, we employ a recently efficient circulant embedding technique. This technique involves absorbing a smooth relaxation of the constraint set into the likelihood, a prior distribution, and elliptical slice sampling (ESS). Our contribution in this article is threefold. First, we extend this technique to address sets of linear, quadratic and nonlinear inequalities, enabling the incorporation of more general and multiple shape constraints. These constraints can be applied individually, jointly, and sequentially. Furthermore,this generalization allows the proposed approach to be easily adapted to other basis functions and models. Second, we explore efficient samplers to approximate both the posterior and prior distributions, including Hamiltonian Monte Carlo and the Fast Fourier Transform. Furthermore, we employ a highly efficient, large-scale approach for sampling from the prior distribution, resulting in significant computational advantages. Third, we investigate the capability of this approach to handle higher-dimensional input spaces and manage a large number of observations. The proposed approach demonstrates flexibility, accuracy, and efficiency in both synthetic and real data studies. |
| نوع الوثيقة: | report |
| اللغة: | English |
| Relation: | hal-04496474; https://hal.science/hal-04496474; https://hal.science/hal-04496474/document; https://hal.science/hal-04496474/file/Efficient_Bayesian_CGP.pdf |
| الاتاحة: | https://hal.science/hal-04496474 https://hal.science/hal-04496474/document https://hal.science/hal-04496474/file/Efficient_Bayesian_CGP.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.6553242E |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |