Web: http://arxiv.org/abs/2108.12515

June 23, 2022, 1:11 a.m. | Maarten V. de Hoop, Nikola B. Kovachki, Nicholas H. Nelsen, Andrew M. Stuart

cs.LG updates on arXiv.org arxiv.org

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

arxiv convergence data learning linear math operators

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