Finite-dimensional approximation of Gaussian processes with linear inequality constraints and noisy observations
Résumé
Due to their flexibility, Gaussian processes (GPs) have been widely used in non- parametric function estimation. A prior information about the underlying function is often available. In this paper, the finite-dimensional Gaussian approach (Maatouk and Bay, 2017) which can satisfy linear inequality conditions everywhere (e.g. mono- tonicity, convexity and boundary) is considered. In a variety of real-world problems, the observed data usually possess noise. In this paper, this approach has been ex- tended to deal with noisy observations. The mean and the maximum of the posterior distribution are well defined. Additionally, to simulate from the posterior distribu- tion two methods have been used: the exact rejection sampling from the Mode and the Hamiltonian Monte Carlo method which is more efficient in high-dimensional cases. The generalization of the Kimeldorf-Wahba correspondence Kimeldorf and Wahba (1970) is proved in noisy observation cases. A comparison shown that the proposed model outperforms all recent models dealing with the same constraints in terms of predictive accuracy and coverage intervals.
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