Institut de Mathématiques de Toulouse

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Séminaire de Statistique

par Agnès Lagnoux - publié le , mis à jour le

Organisateurs : Agnès Lagnoux, Jean-Marc Azais et François Bachoc

Jour et lieu habituels : le mardi à 11h00 en salle 106 (bâtiment 1R1).

  • Mardi 23 janvier 11:00-12:00 - Andrès Felipe Lopez Lopera - Mines Saint Etienne & IMT

    Gaussian process regression models under linear inequality conditions

    Résumé : In the last decades, Gaussian processes (GPs) have become one of the most attractive Bayesian framework due to their ability to perform both regression and classification tasks. However, due to their pure data-driven nature, they do not account for the physical properties exhibited in real-world data (e.g. positivity, monotonicity), which can lead to more realistic data interpolation and uncertainty quantifications. Our aim is to investigate deeper GP regression models under inequality constraints. Based on a finite-dimensional approximation, our contributions are threefold. First, we propose a GP regression model which can deal with any linear inequality constraint. Second, we suggest an efficient Hamiltonian Monte Carlo-based sampler to approximate the posterior distribution satisfying both interpolation and inequality conditions. Finally, we investigate theoretical and numerical properties of a constrained likelihood for covariance parameter estimation. The model is tested under both synthetic and real-world data in 1D or 2D.