Séminaire MODAL'X : Eddy Ella Mintsa (AgroParisTech)

Résumé : Recent advents in modern technology have generated labeled data recorded at high frequency, that can be modelled as functional data. This work focuses on multiclass classification problem for functional data modelled by a stochastic differential equation. Few works study the case where functional data are modelled by diffusion processes, which is why the construction of classification procedures adapted to this type of model is a major challenge. We focus on time-homogeneous stochastic differential equations with unknown and non-parametric drift and diffusion coefficients. The objective is to propose an implementable classification procedure based on the minimization of the empirical risk of misclassification. For the resulting classification procedure to be implementable, we proceed to the convexification of the model, replacing both the loss function and the set of classifiers by convex surrogates. We then establish the consistency of the obtained empirical classifier and derive some rates of convergence over the Hölder space. The theoretical study is completed with a numerical illustration over simulated data.