# Pairwise Ranking with Gaussian Kernels

arXiv: https://arxiv.org/abs/2304.03185 · HTML: https://mlsanity.com/paper/2304.03185/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 52 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 3 of 3)

- [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)
- [Estimation error analysis of deep learning on the regression problem on the variable exponent Besov space](https://mlsanity.com/paper/2009.11285/) (2020)
- [Oracle inequalities for ranking and U-processes with Lasso penalty](https://mlsanity.com/paper/1512.05698/) (2015)

## Built on by (most cited first, 2 of 2)

- [Solving PDEs on Spheres with Physics-Informed Convolutional Neural Networks](https://mlsanity.com/paper/2308.09605/) (2023)
- [Fine-grained Analysis of Non-parametric Estimation for Pairwise Learning](https://mlsanity.com/paper/2305.19640/) (2023)

## Abstract (arXiv)

Regularized pairwise ranking with Gaussian kernels is one of the cutting-edge learning algorithms. Despite a wide range of applications, a rigorous theoretical demonstration still lacks to support the performance of such ranking estimators. This work aims to fill this gap by developing novel oracle inequalities for regularized pairwise ranking. With the help of these oracle inequalities, we derive fast learning rates of Gaussian ranking estimators under a general box-counting dimension assumption on the input domain combined with the noise conditions or the standard smoothness condition. Our theoretical analysis improves the existing estimates and shows that a low intrinsic dimension of input space can help the rates circumvent the curse of dimensionality.