# Sparse Kernel Gaussian Processes through Iterative Charted Refinement (ICR)

arXiv: https://arxiv.org/abs/2206.10634 · HTML: https://mlsanity.com/paper/2206.10634/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 21 Jun 2022.

## Builds on (most cited first, 15 of 15)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [Constant-Time Predictive Distributions for Gaussian Processes](https://mlsanity.com/paper/1803.06058/) (2018)
- [Thoughts on Massively Scalable Gaussian Processes](https://mlsanity.com/paper/1511.01870/) (2015)
- [Fast Matrix Square Roots with Applications to Gaussian Processes and Bayesian Optimization](https://mlsanity.com/paper/2006.11267/) (2020)
- [Automatic Differentiation Variational Inference with Mixtures](https://mlsanity.com/paper/2003.01687/) (2020)
- [Metric Gaussian Variational Inference](https://mlsanity.com/paper/1901.11033/) (2019)
- [Geometric variational inference](https://mlsanity.com/paper/2105.10470/) (2021)
- [Optimal Belief Approximation](https://mlsanity.com/paper/1610.09018/) (2016)
- [The Galactic 3D large-scale dust distribution via Gaussian process regression on spherical coordinates](https://mlsanity.com/paper/2204.11715/) (2022)

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

- [Re-Envisioning Numerical Information Field Theory (NIFTy.re): A Library for Gaussian Processes and Variational Inference](https://mlsanity.com/paper/2402.16683/) (2024)
- [GraphGP: Scalable Gaussian Processes with Vecchia's Approximation](https://mlsanity.com/paper/2606.11402/) (2026)

## Abstract (arXiv)

Gaussian Processes (GPs) are highly expressive, probabilistic models. A major limitation is their computational complexity. Naively, exact GP inference requires O(N3) computations with N denoting the number of modeled points. Current approaches to overcome this limitation either rely on sparse, structured or stochastic representations of data or kernel respectively and usually involve nested optimizations to evaluate a GP. We present a new, generative method named Iterative Charted Refinement (ICR) to model GPs on nearly arbitrarily spaced points in O(N) time for decaying kernels without nested optimizations. ICR represents long- as well as short-range correlations by combining views of the modeled locations at varying resolutions with a user-provided coordinate chart. In our experiment with points whose spacings vary over two orders of magnitude, ICR's accuracy is comparable to state-of-the-art GP methods. ICR outperforms existing methods in terms of computational speed by one order of magnitude on the CPU and GPU and has already been successfully applied to model a GP with 122 billion parameters.