A1277
Title: Infinite-dimensional spherical kernel ridge regression
Authors: Beatrice Matteo - University of Geneva (Switzerland) [presenting]
Abstract: A new regression framework for nonlinear modeling of responses that lie on Hilbert spheres, in both finite and infinite dimensions, is introduced. Unlike tangent space regression, which lifts all responses to a common tangent space, this approach computes residuals directly on the nonlinear manifold. The tangent space instead acts as the linear predictor space, where the regression function takes values. By combining Riemannian geometry with functional data analysis, the regression function is modeled using tools from vector-valued reproducing kernel Hilbert space theory. This formulation reduces the infinite-dimensional estimation problem to a finite-dimensional one via a representer theorem, and leads to an estimation algorithm based on gradient descent. Explicit, verifiable conditions on the data that guarantee convergence of the algorithm to the global optimum are provided, and the consistency as well as rates of convergence of the proposed estimator are established.
