# Optimal Learning with Anisotropic Gaussian SVMs

arXiv: https://arxiv.org/abs/1810.02321 · HTML: https://mlsanity.com/paper/1810.02321/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2018.

## Built on by (most cited first, 4 of 4)

- [Nested Expectations with Kernel Quadrature](https://mlsanity.com/paper/2502.18284/) (2025)
- [Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learning](https://mlsanity.com/paper/2406.01435/) (2024)
- [Enhancing Kernel Flexibility via Learning Asymmetric Locally-Adaptive Kernels](https://mlsanity.com/paper/2310.05236/) (2023)
- [Perturbative methods for non-parametric instrumental variable](https://mlsanity.com/paper/2606.00322/) (2026)

## Abstract (arXiv)

This paper investigates the nonparametric regression problem using SVMs with anisotropic Gaussian RBF kernels. Under the assumption that the target functions are resided in certain anisotropic Besov spaces, we establish the almost optimal learning rates, more precisely, optimal up to some logarithmic factor, presented by the effective smoothness. By taking the effective smoothness into consideration, our almost optimal learning rates are faster than those obtained with the underlying RKHSs being certain anisotropic Sobolev spaces. Moreover, if the target function depends only on fewer dimensions, faster learning rates can be further achieved.