# Multiresolution Kernel Approximation for Gaussian Process Regression

arXiv: https://arxiv.org/abs/1708.02183 · HTML: https://mlsanity.com/paper/1708.02183/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2017.

## Built on by (most cited first, 6 of 6)

- [Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and More](https://mlsanity.com/paper/2107.06876/) (2021)
- [Fast Temporal Wavelet Graph Neural Networks](https://mlsanity.com/paper/2302.08643/) (2023)
- [NURD: Negative-Unlabeled Learning for Online Datacenter Straggler Prediction](https://mlsanity.com/paper/2203.08339/) (2022)
- [Spatially scalable recursive estimation of Gaussian process terrain maps using local basis functions](https://mlsanity.com/paper/2210.09168/) (2022)
- [Learning Multiresolution Matrix Factorization and its Wavelet Networks on Graphs](https://mlsanity.com/paper/2111.01940/) (2021)
- [Learning to Solve Multiresolution Matrix Factorization by Manifold Optimization and Evolutionary Metaheuristics](https://mlsanity.com/paper/2406.00469/) (2024)

## Abstract (arXiv)

Gaussian process regression generally does not scale to beyond a few thousands data points without applying some sort of kernel approximation method. Most approximations focus on the high eigenvalue part of the spectrum of the kernel matrix, K, which leads to bad performance when the length scale of the kernel is small. In this paper we introduce Multiresolution Kernel Approximation (MKA), the first true broad bandwidth kernel approximation algorithm. Important points about MKA are that it is memory efficient, and it is a direct method, which means that it also makes it easy to approximate K-1 and mathoptextrmdet(K).