# Regularization of Statistical Inverse Problems on Non-Reflexive Banach Spaces

arXiv: https://arxiv.org/abs/2608.17533 · HTML: https://mlsanity.com/paper/2608.17533/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 18 Aug 2026.

## Builds on (most cited first, 4 of 4)

- [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)
- [Learning sparsity-promoting regularizers for linear inverse problems](https://mlsanity.com/paper/2412.16031/) (2024)
- [Convergence Analysis of Statistical Inverse Problems on Reproducing Kernel Banach Spaces](https://mlsanity.com/paper/2608.16404/) (2026)

## Abstract (arXiv)

Inverse learning within a statistical framework has a wide range of applications. It has garnered significant attention in machine learning, artificial intelligence, and related fields, where the goal is to infer unknown parameters from indirect and noisy observations. This work investigates the stable approximation of udagger which solves the equation Au=g, with A being a linear operator between appropriate vector spaces. We will consider the domain to be a non-reflexive Banach Space and the co-domain to be a space of real-valued functions on a metric space X. The function g is characterized by a finite number of independently and identically distributed data points, which are assumed to follow some unknown probability measure ρ. We employ Tikhonov regularization with an arbitrary convex functional to obtain the regularized solution corresponding to the given data point. The convergence analysis is carried out with respect to the Bregman distance, and an upper bound for the error is derived in probability terms. The theoretical findings are then supported by numerical experiments.