Posterior Contraction of L\'evy Adaptive B-spline Regression in Besov Spaces
Authors: Jeunghun Oh, Sewon Park, Jaeyong Lee
Summary
arXiv:2605. 19610v1 Announce Type: new Abstract: 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.
Relevance
Read next because Posterior Contraction of L'evy Adaptive B-spline Regression in Besov Spaces overlaps with clean result "LoRA persona trained on alone emits at 23.5% when a co-trained partner learns ..., vs 0% control on Qwen2.5-7B-Instruct (MODERATE confidence)", clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)". Matching terms: fill, class, line, rate, factor, test, model. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.19610v1 Announce Type: new Abstract: 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.