# Bayesian Nonparametric Kernel-Learning

arXiv: https://arxiv.org/abs/1506.08776 · HTML: https://mlsanity.com/paper/1506.08776/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2015.

## Built on by (most cited first, 10 of 10)

- [On Learning the Transformer Kernel](https://mlsanity.com/paper/2110.08323/) (2021)
- [Federated Bayesian Neural Regression: A Scalable Global Federated Gaussian Process](https://mlsanity.com/paper/2206.06357/) (2022)
- [Spectraformer: A Unified Random Feature Framework for Transformer](https://mlsanity.com/paper/2405.15310/) (2024)
- [Marginalising over Stationary Kernels with Bayesian Quadrature](https://mlsanity.com/paper/2106.07452/) (2021)
- [Bayesian Non-linear Latent Variable Modeling via Random Fourier Features](https://mlsanity.com/paper/2306.08352/) (2023)
- [Preventing Model Collapse in Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2404.01697/) (2024)
- [Modelling Non-Smooth Signals with Complex Spectral Structure](https://mlsanity.com/paper/2203.06997/) (2022)
- [Sparse Infinite Random Feature Latent Variable Modeling](https://mlsanity.com/paper/2205.09909/) (2022)
- [Combining Bayesian Inference and Reinforcement Learning for Agent Decision Making: A Review](https://mlsanity.com/paper/2505.07911/) (2025)
- [Scalable Random Feature Latent Variable Models](https://mlsanity.com/paper/2410.17700/) (2024)

## Abstract (arXiv)

Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample estimator may be greatly affected by the choice of kernel. Furthermore, when directly applying kernel methods, one typically needs to compute a N × N Gram matrix of pairwise kernel evaluations to work with a dataset of N instances. The computation of this Gram matrix precludes the direct application of kernel methods on large datasets, and makes kernel learning especially difficult. In this paper we introduce Bayesian nonparmetric kernel-learning (BaNK), a generic, data-driven framework for scalable learning of kernels. BaNK places a nonparametric prior on the spectral distribution of random frequencies allowing it to both learn kernels and scale to large datasets. We show that this framework can be used for large scale regression and classification tasks. Furthermore, we show that BaNK outperforms several other scalable approaches for kernel learning on a variety of real world datasets.