Convergence Rates for Learning Linear Operators from Noisy Data. (arXiv:2108.12515v2 [math.ST] UPDATED)

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

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