# Distributed Learning via Filtered Hyperinterpolation on Manifolds

arXiv: https://arxiv.org/abs/2007.09392 · HTML: https://mlsanity.com/paper/2007.09392/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [Spherical Analysis of Learning Nonlinear Functionals](https://mlsanity.com/paper/2410.01047/) (2024)

## Abstract (arXiv)

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.