# Adaptive Bayesian Multivariate Spline Knot Inference with Prior Specifications on Model Complexity

arXiv: https://arxiv.org/abs/2405.13353 · HTML: https://mlsanity.com/paper/2405.13353/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 50 references that are in the map.
- First posted on arXiv 22 May 2024.

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

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Manifold Fitting under Unbounded Noise](https://mlsanity.com/paper/1909.10228/) (2019)
- [Image Response Regression via Deep Neural Networks](https://mlsanity.com/paper/2006.09911/) (2020)
- [Multivariate Spline Estimation and Inference for Image-On-Scalar Regression](https://mlsanity.com/paper/2106.01431/) (2021)

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

- [Adversarial Robustness of Nonparametric Regression](https://mlsanity.com/paper/2505.17356/) (2025)

## Abstract (arXiv)

In multivariate spline regression, the number and locations of knots influence the performance and interpretability significantly. However, due to non-differentiability and varying dimensions, there is no desirable frequentist method to make inference on knots. In this article, we propose a fully Bayesian approach for knot inference in multivariate spline regression. The existing Bayesian method often uses BIC to calculate the posterior, but BIC is too liberal and it will heavily overestimate the knot number when the candidate model space is large. We specify a new prior on the knot number to take into account the complexity of the model space and derive an analytic formula in the normal model. In the non-normal cases, we utilize the extended Bayesian information criterion to approximate the posterior density. The samples are simulated in the space with differing dimensions via reversible jump Markov chain Monte Carlo. We apply the proposed method in knot inference and manifold denoising. Experiments demonstrate the splendid capability of the algorithm, especially in function fitting with jumping discontinuity.