Operator-valued Kernels for Learning from Functional Response Data

By Hachem Kadri, Emmanuel Duflos, Philippe Preux, Stéphane Canu, Alain Rakotomamonjy, Julien Audiffren. 2015

154 citations recorded by the source corpus.

In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basic concepts and properties of kernel-based learning are extended to include the estimation of function-valued functions. In this setting, the representer theorem is restated, a set of rigorously defined infinite-dimensional operator-valued kernels that can be valuably applied when the data are functions is described, and a learning algorithm for nonlinear functional data analysis is introduced. The methodology is illustrated through speech and audio signal processing experiments.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Control and Systems Engineering

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Citations in the corpus

Learning Theory for Distribution Regression (2014, background): “Although the primary contribution of our paper is theoretical, some illustrative numerical examples are given in Section 6.”
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets (2021, unknown): “Beyond deep learning approaches, operator-valued kernel methods [36, 37] have also been demonstrated as a powerful tool for learning nonlinear operators, and they can naturally be generalized to neural networks acting on function spaces [38], but their applicability is generally limited due to their”