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Estimation of Riemannian distances between covariance operators and Gaussian processes
In this work we study two Riemannian distances between infinite-dimensional positive definite Hilbert-Schmidt operators, namely affine-invariant Riemannian and Log-Hilbert-Schmidt distances, in the context of covariance operators associated with functional stochastic processes, in particular Gaussian processes.
Operator-Valued Bochner Theorem, Fourier Feature Maps for Operator-Valued Kernels, and Vector-Valued Learning
Our general setting is that of operator-valued kernels corresponding to RKHS of functions with values in a Hilbert space.
Approximate Log-Hilbert-Schmidt Distances Between Covariance Operators for Image Classification
This paper presents a novel framework for visual object recognition using infinite-dimensional covariance operators of input features, in the paradigm of kernel methods on infinite-dimensional Riemannian manifolds.
Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems.
A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learning
This paper presents a general vector-valued reproducing kernel Hilbert spaces (RKHS) framework for the problem of learning an unknown functional dependency between a structured input space and a structured output space.
