# Inverse learning in Hilbert scales

arXiv: https://arxiv.org/abs/2002.10208 · HTML: https://mlsanity.com/paper/2002.10208/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2020.

## Built on by (most cited first, 5 of 5)

- [Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfer](https://mlsanity.com/paper/2501.10870/) (2025)
- [Statistical inverse learning problems with random observations](https://mlsanity.com/paper/2312.15341/) (2023)
- [Statistical Inverse Problems in Hilbert Scales](https://mlsanity.com/paper/2208.13289/) (2022)
- [Minimax Rates and Spectral Distillation for Tree Ensembles](https://mlsanity.com/paper/2605.11841/) (2026)
- [Statistical inverse learning and ℓ1-regularization](https://mlsanity.com/paper/2607.07468/) (2026)

## Abstract (arXiv)

We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of convergence for the regularized solution under the prior assumptions and a certain link condition. We express the error in terms of certain distance functions. For regression functions with smoothness given in terms of source conditions the error bound can then be explicitly established.