MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Distributed Learning via Filtered Hyperinterpolation on Manifolds

Guido Montúfar and Yu Guang Wang


Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the problem of learning real-valued functions on manifolds through filtered hyperinterpolation of input-output data pairs where the inputs may be sampled deterministically or at random and the outputs may be clean or noisy. Motivated by the problem of handling large data sets, it presents a parallel data processing approach which distributes the data-fitting task among multiple servers and synthesizes the fitted sub-models into a global estimator. We prove quantitative relations between the approximation quality of the learned function over the entire manifold, the type of target function, the number of servers, and the number and type of available samples. We obtain the approximation rates of convergence for distributed and non-distributed approaches. For the non-distributed case, the approximation order is optimal.

Jul 18, 2020
Jul 18, 2020
Distributed learning, Filtered hyperinterpolation, Approximation on manifolds, Kernel methods, Numerical integration on manifolds, Quadrature rule, Random sampling, Gaussian white noise

Related publications

2022 Journal Open Access
Guido Montúfar and Yu Guang Wang

Distributed learning via filtered hyperinterpolation on manifolds

In: Foundations of computational mathematics, 22 (2022) 4, pp. 1219-1271