# Posterior Contraction of L'evy Adaptive B-spline Regression in Besov Spaces

arXiv: https://arxiv.org/abs/2605.19610 · HTML: https://mlsanity.com/paper/2605.19610/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 34 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 5 of 5)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality](https://mlsanity.com/paper/1810.08033/) (2018)
- [Asymptotic Properties for Bayesian Neural Network in Besov Space](https://mlsanity.com/paper/2206.00241/) (2022)
- [Adaptive Bayesian procedures using random series priors](https://mlsanity.com/paper/1403.0625/) (2014)
- [L'evy Adaptive B-spline Regression via Overcomplete Systems](https://mlsanity.com/paper/2101.12179/) (2021)

## Abstract (arXiv)

We investigate the asymptotic properties of the L'evy Adaptive B-spline (LABS) regression model, a Bayesian nonparametric method that incorporates B-spline kernels into the L'evy Adaptive Regression Kernel (LARK) model. LABS applies splines of varying degrees with independently defined knots, yielding a flexible model class capable of adapting to irregular and locally structured features of the true function. Within the nonparametric regression framework with univariate random design and Gaussian errors, we establish that the LABS posterior contracts around the true function in Besov classes at nearly minimax-optimal rates, up to a logarithmic factor, while adapting automatically to unknown smoothness. This study contributes to filling a gap in the literature, where theoretical results on posterior contraction of the LARK model in Besov spaces remain scarce. Simulation experiments on standard test functions in Besov spaces, including Blocks, Bumps, HeaviSine, and Doppler, complement the theoretical results and demonstrate the practical utility of LABS.