This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs random input vectors in a space and their noisy images under an unknown self-adjoint operator. Assuming that operator is diagonalizable known basis, this work solves equivalent inverse problem estimating operator’s eigenvalues given data. Adopting Bayesian approach,...

The intrinsic nature of noisy and complex data sets is often concealed in low-dimensional structures embedded a higher dimensional space. Number methodologies have been developed to extract represent such the form manifolds (i.e. geometric that locally resemble continuously deformable intervals Rj1). Usually a-priori knowledge manifold's dimensionality required. Additionally, their performance ...