# Learning Data-adaptive Nonparametric Kernels

arXiv: https://arxiv.org/abs/1808.10724 · HTML: https://mlsanity.com/paper/1808.10724/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2018.

## Built on by (most cited first, 7 of 7)

- [On Learning the Transformer Kernel](https://mlsanity.com/paper/2110.08323/) (2021)
- [Heterogeneous Treatment Effect with Trained Kernels of the Nadaraya-Watson Regression](https://mlsanity.com/paper/2207.09139/) (2022)
- [Kernel Biclustering algorithm in Hilbert Spaces](https://mlsanity.com/paper/2208.03675/) (2022)
- [Weighted Neural Tangent Kernel: A Generalized and Improved Network-Induced Kernel](https://mlsanity.com/paper/2103.11558/) (2021)
- [BENK: The Beran Estimator with Neural Kernels for Estimating the Heterogeneous Treatment Effect](https://mlsanity.com/paper/2211.10793/) (2022)
- [Enhancing Kernel Flexibility via Learning Asymmetric Locally-Adaptive Kernels](https://mlsanity.com/paper/2310.05236/) (2023)
- [Data Imputation by Pursuing Better Classification: A Supervised Kernel-Based Method](https://mlsanity.com/paper/2405.07800/) (2024)

## Abstract (arXiv)

In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise scheme. Learning this data-adaptive matrix in a formulation-free strategy enlarges the margin between classes and thus improves the model flexibility. The introduced two constraints are imposed either exactly (on small data sets) or approximately (on large data sets) in our model, which provides a controllable trade-off between model flexibility and complexity with theoretical demonstration. In algorithm optimization, the objective function of our learning framework is proven to be gradient-Lipschitz continuous. Thereby, kernel and classifier/regressor learning can be efficiently optimized in a unified framework via Nesterov's acceleration. For the scalability issue, we study a decomposition-based approach to our model in the large sample case. The effectiveness of this approximation is illustrated by both empirical studies and theoretical guarantees. Experimental results on various classification and regression benchmark data sets demonstrate that our non-parametric kernel learning framework achieves good performance when compared with other representative kernel learning based algorithms.