# Fast Gaussian Process Posterior Mean Prediction via Local Cross Validation and Precomputation

arXiv: https://arxiv.org/abs/2205.10879 · HTML: https://mlsanity.com/paper/2205.10879/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 61 references that are in the map.
- First posted on arXiv 22 May 2022.

## Builds on (most cited first, 21 of 21)

- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Reinforcement Learning in Healthcare: A Survey](https://mlsanity.com/paper/1908.08796/) (2019)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [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)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [A Case Study Competition Among Methods for Analyzing Large Spatial Data](https://mlsanity.com/paper/1710.05013/) (2017)
- [The Variational Gaussian Process](https://mlsanity.com/paper/1511.06499/) (2015)
- [Learning Scalable Deep Kernels with Recurrent Structure](https://mlsanity.com/paper/1610.08936/) (2016)
- [Distributed Variational Inference in Sparse Gaussian Process Regression and Latent Variable Models](https://mlsanity.com/paper/1402.1389/) (2014)
- [Locally induced Gaussian processes for large-scale simulation experiments](https://mlsanity.com/paper/2008.12857/) (2020)
- [Asynchronous Distributed Variational Gaussian Processes for Regression](https://mlsanity.com/paper/1704.06735/) (2017)
- [MuyGPs: Scalable Gaussian Process Hyperparameter Estimation Using Local Cross-Validation](https://mlsanity.com/paper/2104.14581/) (2021)
- [On Random Subsampling of Gaussian Process Regression: A Graphon-Based Analysis](https://mlsanity.com/paper/1901.09541/) (2019)
- [Gaussian Process Models with Parallelization and GPU acceleration](https://mlsanity.com/paper/1410.4984/) (2014)
- [Spectral Density Estimation for Random Fields via Periodic Embeddings](https://mlsanity.com/paper/1710.08978/) (2017)
- [Forecasting of commercial sales with large scale Gaussian Processes](https://mlsanity.com/paper/1709.05548/) (2017)

## Built on by (most cited first, 1 of 1)

- [Light curve completion and forecasting using fast and scalable Gaussian processes (MuyGPs)](https://mlsanity.com/paper/2208.14592/) (2022)

## Abstract (arXiv)

Gaussian processes (GPs) are Bayesian non-parametric models useful in a myriad of applications. Despite their popularity, the cost of GP predictions (quadratic storage and cubic complexity with respect to the number of training points) remains a hurdle in applying GPs to large data. We present a fast posterior mean prediction algorithm called FastMuyGPs to address this shortcoming. FastMuyGPs is based upon the MuyGPs hyperparameter estimation algorithm and utilizes a combination of leave-one-out cross-validation, batching, nearest neighbors sparsification, and precomputation to provide scalable, fast GP prediction. We demonstrate several benchmarks wherein FastMuyGPs prediction attains superior accuracy and competitive or superior runtime to both deep neural networks and state-of-the-art scalable GP algorithms.