Approximation Theory, Computing, and Deep Learning on the Wasserstein Space

arXiv:2310.19548v3 Announce Type: replace-cross
Abstract: The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. In this study, we delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on probability spaces. Our particular focus centers on the Wasserstein distance function, which serves as a relevant example. In contrast to the existing body of literature focused on approximating efficiently pointwise evaluations, we chart a new course to define functional approximants by …

abstract approximation arxiv challenge computing cs.lg deep learning focus function functions math.fa math.oc numerical probability samples space spaces study theory type