# Convergence Analysis of Statistical Inverse Problems on Reproducing Kernel Banach Spaces

arXiv: https://arxiv.org/abs/2608.16404 · HTML: https://mlsanity.com/paper/2608.16404/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 33 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Builds on (most cited first, 2 of 2)

- [Optimal Rates For Regularization Of Statistical Inverse Learning Problems](https://mlsanity.com/paper/1604.04054/) (2016)
- [Sparse Representer Theorems for Learning in Reproducing Kernel Banach Spaces](https://mlsanity.com/paper/2305.12584/) (2023)

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

- [Regularization of Statistical Inverse Problems on Non-Reflexive Banach Spaces](https://mlsanity.com/paper/2608.17533/) (2026)

## Abstract (arXiv)

Statistical inverse problems have garnered significant attention in recent years due to the growing importance of statistical learning theory and functional analytic approaches in the fields of machine learning and artificial intelligence. In this paper, we investigate the stable approximation of the element udagger that satisfies the equation Au = g, where A is a linear operator that maps a Banach space into an appropriate function space. The function g is observed only through independently and identically distributed data points that are corrupted by noise and assumed to follow an unknown distribution ρ. We employ the Tikhonov regularization scheme, leveraging statistical learning techniques and the framework of reproducing kernel Banach spaces to estimate the solution. We establish convergence and derive the convergence rate of the estimated solution with respect to the true solution as the number of data points increases, with the rate expressed in probabilistic terms. The theoretical findings are further supported by numerical experiments that demonstrate the effectiveness of the proposed approach.